<\/span> \u0645\u0627 \u0647\u0648 \u0645\u0632\u064a\u062c \u062e\u0637\u064a \u0645\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a\u061f<\/span><\/h2>\n \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u062a\u0631\u0643\u064a\u0628\u0629 \u0627\u0644\u062e\u0637\u064a\u0629 \u0647\u0648 \u0643\u0645\u0627 \u064a\u0644\u064a: <\/p>\n
\n<\/div>\n<\/div>\n\n \u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0629 \u0627\u0644\u062e\u0637\u064a\u0629<\/strong> \u0644\u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0647\u064a \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0630\u064a \u064a\u062a\u0645 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u064a\u0647 \u0639\u0646 \u0637\u0631\u064a\u0642 \u0625\u0636\u0627\u0641\u0629 \u062c\u0645\u064a\u0639 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0641\u064a \u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0636\u0631\u0648\u0628\u0629 \u0641\u064a \u0627\u0644\u0643\u0645\u064a\u0627\u062a \u0627\u0644\u0642\u064a\u0627\u0633\u064a\u0629 (\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u062d\u0642\u064a\u0642\u064a\u0629).<\/p>\n \u0648\u0628\u0639\u0628\u0627\u0631\u0629 \u0623\u062e\u0631\u0649\u060c \u0646\u0638\u0631\u0627 \u0644\u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a<\/p>\n
\n
![\"\\vv{\\text{v}}_1,](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-33729e6d20b00643b5d9ddf38544c11c_l3.png\" "\\"Rendered")
<\/p>\n
\u0645\u0632\u064a\u062c \u062e\u0637\u064a \u0645\u0646\u0647\u0645 \u0633\u064a\u0643\u0648\u0646:<\/p>\n
\n
![\"\\vv{\\text{w}}=a_1\\vv{\\text{v}}_1+a_2\\vv{\\text{v}}_2+\\dots](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a1fe2e85f82aa1452aa43a172ca8d256_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n
\u062d\u064a\u062b \u0627\u0644\u0645\u0639\u0627\u0645\u0644\u0627\u062a<\/p>\n
\n
![\"a_i\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f91083f3035e5168a6f0b3e6335d6858_l3.png\" "\\"Rendered")
<\/p>\n
\u0647\u0630\u0647 \u0623\u0631\u0642\u0627\u0645 \u062d\u0642\u064a\u0642\u064a\u0629.<\/p>\n<\/div>\n
\u0648\u0645\u0646 \u062b\u0645\u060c \u0641\u0625\u0646 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0630\u064a \u064a\u0643\u0648\u0646 \u0639\u0628\u0627\u0631\u0629 \u0639\u0646 \u0645\u062c\u0645\u0648\u0639\u0629 \u062e\u0637\u064a\u0629 \u0645\u0646 \u0645\u062a\u062c\u0647\u0627\u062a \u0623\u062e\u0631\u0649 \u064a\u0639\u0646\u064a \u0623\u0646\u0647 \u064a\u0645\u0643\u0646 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0639\u0646 \u0627\u0644\u0623\u0648\u0644 \u0628\u062f\u0644\u0627\u0644\u0629 \u0627\u0644\u062b\u0627\u0646\u064a.<\/p>\n
\u064a\u0645\u0643\u0646 \u0641\u0647\u0645 \u0647\u0630\u0627 \u0627\u0644\u0645\u0641\u0647\u0648\u0645 \u0628\u0634\u0643\u0644 \u0623\u0641\u0636\u0644 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0631\u0633\u0645 \u0628\u064a\u0627\u0646\u064a \u0644\u0645\u062a\u062c\u0647 \u0641\u064a \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0648\u0647\u0648 \u0639\u0628\u0627\u0631\u0629 \u0639\u0646 \u0645\u0632\u064a\u062c \u062e\u0637\u064a \u0645\u0646 \u0645\u062a\u062c\u0647\u064a\u0646: <\/p>\n
\n![\"\u0645\u062c\u0645\u0648\u0639\u0629](\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/combinaison-lineaire-de-vecteurs-graphique.webp\")
<\/figure>\n<\/div>\n \u0643\u0645\u0627 \u062a\u0631\u0648\u0646 \u0641\u064a \u0627\u0644\u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u064a \u0623\u0639\u0644\u0627\u0647\u060c \u0627\u0644\u0645\u062a\u062c\u0647<\/p>\n
\n
![\"\\vv{\\text{w}}\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3b4bbbc56786695092eac40831aee80d_l3.png\" "\\"Rendered")
<\/p>\n
\u064a\u0645\u0643\u0646 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u064a\u0647\u0627 \u0645\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a<\/p>\n
![\"\\vv{\\text{u}}\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cac24ae79c1e4cbc459f01ed5e4f824e_l3.png\" "\\"Rendered")
<\/p>\n
\u0648<\/p>\n
![\"\\vv{\\text{v}}\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-391ac2e3ba0b7f327ba5a0edc1ba162d_l3.png\" "\\"Rendered")
<\/p>\n
\u062a\u0646\u0641\u064a\u0630 \u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a. \u0648\u0644\u0630\u0644\u0643 \u0641\u0625\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a<\/p>\n
<\/p>\n
\u0639\u0628\u0627\u0631\u0629 \u0639\u0646 \u0645\u0632\u064a\u062c \u062e\u0637\u064a \u0645\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u064a\u0646 \u0627\u0644\u0622\u062e\u0631\u064a\u0646.<\/p>\n
\u064a\u062c\u0628 \u0627\u0644\u062a\u0623\u0643\u064a\u062f \u0639\u0644\u0649 \u0623\u0646 \u0647\u0630\u0647 \u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0629 \u0627\u0644\u062e\u0637\u064a\u0629 \u0641\u0631\u064a\u062f\u0629 \u0645\u0646 \u0646\u0648\u0639\u0647\u0627<\/strong> \u060c \u0623\u0648 \u0628\u0645\u0639\u0646\u0649 \u0622\u062e\u0631\u060c \u0644\u0627 \u064a\u0648\u062c\u062f \u0633\u0648\u0649 \u0645\u062c\u0645\u0648\u0639\u0629 \u062e\u0637\u064a\u0629 \u0648\u0627\u062d\u062f\u0629 \u0645\u0645\u0643\u0646\u0629 \u0644\u0643\u0644 \u0645\u062a\u062c\u0647. \u0644\u0623\u0646\u0647\u060c \u0628\u0627\u062a\u0628\u0627\u0639 \u0627\u0644\u0645\u062b\u0627\u0644 \u0627\u0644\u0633\u0627\u0628\u0642\u060c \u0625\u0630\u0627 \u0636\u0631\u0628\u0646\u0627<\/p>\n\n
<\/p>\n
\u0645\u0642\u0627\u0628\u0644 6 \u0628\u062f\u0644\u0627\u064b \u0645\u0646 4\u060c \u0633\u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \u0645\u062a\u062c\u0647 \u0622\u062e\u0631 \u0645\u062e\u062a\u0644\u0641. <\/p>\n
\n<\/div>\n<\/div>\n \u0639\u0644\u0627\u0648\u0629 \u0639\u0644\u0649 \u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u0625\u062d\u062f\u0649 \u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u062a\u0631\u0643\u064a\u0628 \u0627\u0644\u062e\u0637\u064a \u0641\u064a \u0627\u0644\u0645\u0633\u062a\u0648\u0649 (\u0641\u064a R2) \u0647\u064a \u0623\u0646\u0647 \u064a\u0645\u0643\u0646 \u0648\u0636\u0639 \u0623\u064a \u0645\u062a\u062c\u0647 \u0643\u062f\u0645\u062c \u062e\u0637\u064a \u0644\u0645\u062a\u062c\u0647\u064a\u0646 \u0622\u062e\u0631\u064a\u0646 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0644\u0647\u0645\u0627 \u0627\u062a\u062c\u0627\u0647\u0627\u062a \u0645\u062e\u062a\u0644\u0641\u0629\u060c \u0623\u064a \u0625\u0630\u0627 \u0644\u0645 \u064a\u0643\u0648\u0646\u0627 \u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646.<\/p>\n
\u0648\u0623\u064a\u0636\u064b\u0627\u060c \u0641\u064a \u0628\u0639\u0636 \u0627\u0644\u0623\u062d\u064a\u0627\u0646 \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0644\u062a\u0639\u0631\u0641 \u0628\u0627\u0644\u0639\u064a\u0646 \u0627\u0644\u0645\u062c\u0631\u062f\u0629 \u0639\u0644\u0649 \u0623\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u064a\u0646 \u0639\u0628\u0627\u0631\u0629 \u0639\u0646 \u0645\u062c\u0645\u0648\u0639\u0629 \u062e\u0637\u064a\u0629. \u0644\u0644\u0642\u064a\u0627\u0645 \u0628\u0630\u0644\u0643\u060c \u064a\u0643\u0641\u064a \u0623\u0646 \u062a\u0643\u0648\u0646 \u0645\u0643\u0648\u0646\u0627\u062a\u0647 \u0645\u062a\u0646\u0627\u0633\u0628\u0629<\/strong> . \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a \u0627\u0644\u0645\u062a\u062c\u0647\u064a\u0646 \u0627\u0644\u062a\u0627\u0644\u064a\u064a\u0646 \u0645\u062a\u0646\u0627\u0633\u0628\u0629\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0639\u0628\u0627\u0631\u0629 \u0639\u0646 \u0645\u062c\u0645\u0648\u0639\u0629 \u062e\u0637\u064a\u0629:<\/p>\n\n
![\"\\vv{\\text{u}}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f7e90b69f6225543322e762773bbe775_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n
\n
![\"\\cfrac{3}{1}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-aac41542948764e158ebe590c6b36e67_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n
\u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0629 \u0627\u0644\u062e\u0637\u064a\u0629<\/strong> \u0644\u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0647\u064a \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0630\u064a \u064a\u062a\u0645 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u064a\u0647 \u0639\u0646 \u0637\u0631\u064a\u0642 \u0625\u0636\u0627\u0641\u0629 \u062c\u0645\u064a\u0639 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0641\u064a \u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0636\u0631\u0648\u0628\u0629 \u0641\u064a \u0627\u0644\u0643\u0645\u064a\u0627\u062a \u0627\u0644\u0642\u064a\u0627\u0633\u064a\u0629 (\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u062d\u0642\u064a\u0642\u064a\u0629).<\/p>\n \u0648\u0628\u0639\u0628\u0627\u0631\u0629 \u0623\u062e\u0631\u0649\u060c \u0646\u0638\u0631\u0627 \u0644\u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a<\/p>\n \n \u0645\u0632\u064a\u062c \u062e\u0637\u064a \u0645\u0646\u0647\u0645 \u0633\u064a\u0643\u0648\u0646:<\/p>\n \n \u062d\u064a\u062b \u0627\u0644\u0645\u0639\u0627\u0645\u0644\u0627\u062a<\/p>\n \n \u0647\u0630\u0647 \u0623\u0631\u0642\u0627\u0645 \u062d\u0642\u064a\u0642\u064a\u0629.<\/p>\n<\/div>\n \u0648\u0645\u0646 \u062b\u0645\u060c \u0641\u0625\u0646 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0630\u064a \u064a\u0643\u0648\u0646 \u0639\u0628\u0627\u0631\u0629 \u0639\u0646 \u0645\u062c\u0645\u0648\u0639\u0629 \u062e\u0637\u064a\u0629 \u0645\u0646 \u0645\u062a\u062c\u0647\u0627\u062a \u0623\u062e\u0631\u0649 \u064a\u0639\u0646\u064a \u0623\u0646\u0647 \u064a\u0645\u0643\u0646 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0639\u0646 \u0627\u0644\u0623\u0648\u0644 \u0628\u062f\u0644\u0627\u0644\u0629 \u0627\u0644\u062b\u0627\u0646\u064a.<\/p>\n \u064a\u0645\u0643\u0646 \u0641\u0647\u0645 \u0647\u0630\u0627 \u0627\u0644\u0645\u0641\u0647\u0648\u0645 \u0628\u0634\u0643\u0644 \u0623\u0641\u0636\u0644 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0631\u0633\u0645 \u0628\u064a\u0627\u0646\u064a \u0644\u0645\u062a\u062c\u0647 \u0641\u064a \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0648\u0647\u0648 \u0639\u0628\u0627\u0631\u0629 \u0639\u0646 \u0645\u0632\u064a\u062c \u062e\u0637\u064a \u0645\u0646 \u0645\u062a\u062c\u0647\u064a\u0646: <\/p>\n \u0643\u0645\u0627 \u062a\u0631\u0648\u0646 \u0641\u064a \u0627\u0644\u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u064a \u0623\u0639\u0644\u0627\u0647\u060c \u0627\u0644\u0645\u062a\u062c\u0647<\/p>\n \n \u064a\u0645\u0643\u0646 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u064a\u0647\u0627 \u0645\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a<\/p>\n \u0648<\/p>\n \u062a\u0646\u0641\u064a\u0630 \u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a. \u0648\u0644\u0630\u0644\u0643 \u0641\u0625\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a<\/p>\n \u0639\u0628\u0627\u0631\u0629 \u0639\u0646 \u0645\u0632\u064a\u062c \u062e\u0637\u064a \u0645\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u064a\u0646 \u0627\u0644\u0622\u062e\u0631\u064a\u0646.<\/p>\n \u064a\u062c\u0628 \u0627\u0644\u062a\u0623\u0643\u064a\u062f \u0639\u0644\u0649 \u0623\u0646 \u0647\u0630\u0647 \u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0629 \u0627\u0644\u062e\u0637\u064a\u0629 \u0641\u0631\u064a\u062f\u0629 \u0645\u0646 \u0646\u0648\u0639\u0647\u0627<\/strong> \u060c \u0623\u0648 \u0628\u0645\u0639\u0646\u0649 \u0622\u062e\u0631\u060c \u0644\u0627 \u064a\u0648\u062c\u062f \u0633\u0648\u0649 \u0645\u062c\u0645\u0648\u0639\u0629 \u062e\u0637\u064a\u0629 \u0648\u0627\u062d\u062f\u0629 \u0645\u0645\u0643\u0646\u0629 \u0644\u0643\u0644 \u0645\u062a\u062c\u0647. \u0644\u0623\u0646\u0647\u060c \u0628\u0627\u062a\u0628\u0627\u0639 \u0627\u0644\u0645\u062b\u0627\u0644 \u0627\u0644\u0633\u0627\u0628\u0642\u060c \u0625\u0630\u0627 \u0636\u0631\u0628\u0646\u0627<\/p>\n \n \u0645\u0642\u0627\u0628\u0644 6 \u0628\u062f\u0644\u0627\u064b \u0645\u0646 4\u060c \u0633\u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \u0645\u062a\u062c\u0647 \u0622\u062e\u0631 \u0645\u062e\u062a\u0644\u0641. <\/p>\n \u0639\u0644\u0627\u0648\u0629 \u0639\u0644\u0649 \u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u0625\u062d\u062f\u0649 \u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u062a\u0631\u0643\u064a\u0628 \u0627\u0644\u062e\u0637\u064a \u0641\u064a \u0627\u0644\u0645\u0633\u062a\u0648\u0649 (\u0641\u064a R2) \u0647\u064a \u0623\u0646\u0647 \u064a\u0645\u0643\u0646 \u0648\u0636\u0639 \u0623\u064a \u0645\u062a\u062c\u0647 \u0643\u062f\u0645\u062c \u062e\u0637\u064a \u0644\u0645\u062a\u062c\u0647\u064a\u0646 \u0622\u062e\u0631\u064a\u0646 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0644\u0647\u0645\u0627 \u0627\u062a\u062c\u0627\u0647\u0627\u062a \u0645\u062e\u062a\u0644\u0641\u0629\u060c \u0623\u064a \u0625\u0630\u0627 \u0644\u0645 \u064a\u0643\u0648\u0646\u0627 \u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646.<\/p>\n \u0648\u0623\u064a\u0636\u064b\u0627\u060c \u0641\u064a \u0628\u0639\u0636 \u0627\u0644\u0623\u062d\u064a\u0627\u0646 \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0644\u062a\u0639\u0631\u0641 \u0628\u0627\u0644\u0639\u064a\u0646 \u0627\u0644\u0645\u062c\u0631\u062f\u0629 \u0639\u0644\u0649 \u0623\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u064a\u0646 \u0639\u0628\u0627\u0631\u0629 \u0639\u0646 \u0645\u062c\u0645\u0648\u0639\u0629 \u062e\u0637\u064a\u0629. \u0644\u0644\u0642\u064a\u0627\u0645 \u0628\u0630\u0644\u0643\u060c \u064a\u0643\u0641\u064a \u0623\u0646 \u062a\u0643\u0648\u0646 \u0645\u0643\u0648\u0646\u0627\u062a\u0647 \u0645\u062a\u0646\u0627\u0633\u0628\u0629<\/strong> . \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a \u0627\u0644\u0645\u062a\u062c\u0647\u064a\u0646 \u0627\u0644\u062a\u0627\u0644\u064a\u064a\u0646 \u0645\u062a\u0646\u0627\u0633\u0628\u0629\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0639\u0628\u0627\u0631\u0629 \u0639\u0646 \u0645\u062c\u0645\u0648\u0639\u0629 \u062e\u0637\u064a\u0629:<\/p>\n \n \n<\/p>\n<\/p>\n<\/p>\n<\/p>\n<\/figure>\n<\/div>\n<\/p>\n<\/p>\n<\/p>\n<\/p>\n<\/p>\n<\/p>\n<\/p>\n<\/p>\n<\/p>\n
![\"\\vv{\\text{x}}\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-88e41d561c3898029b7b94d7014c1e79_l3.png\" "\\"Rendered")
<\/p>\n![\"\\vv{\\text{u}},](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4b6be5a59bbf478047e4f3ace338ee48_l3.png\" "\\"Rendered")
<\/p>\n![\"\\vv{\\text{w}}.\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d8af8ced46d93e73dc5290e0cca4dc6b_l3.png\" "\\"Rendered")
<\/p>\n<\/li>\n<\/ul>\n![\"\\vv{\\text{x}}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7c6a832874f83ba4de52e88fdd6ed48a_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\vv{\\text{u}}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-746bff339baec38ef705a9ede42411cc_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"a_1\\vv{\\text{u}}+a_2\\vv{\\text{v}}+](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-06d3d6ec5ca4921b109f8f974e73cbbd_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"a_1,](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41a350e61a3992febcf5f69fdb79f79a_l3.png\" "\\"Rendered")
<\/p>\n![\"a_3\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a4306749a1a62a769b17b849d10edba8_l3.png\" "\\"Rendered")
<\/p>\n![\"a_1\\begin{pmatrix}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d9ed95a00184b48d358ba1b0a2abf105_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\begin{pmatrix}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-626790fc18c5942db14924be2397c9f2_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\begin{pmatrix}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1f8ab5661ba692df579d8e88b6244cdd_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\left.](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8e5fe050102a285a325dcd81d07ef5d5_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\left(](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8aa4e245614f286e0697797a18ba4465_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\left(\\begin{array}{ccc|c}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41f1d9c941fe239bb40297b998eb6929_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\left(](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-02a8a00406479f367627b682099e05c0_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\left.](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-74ed1b18779582d6683ecaa1a9085e3d_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"a_3:\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a5e5ed86162a9b0324b8f44dc16fcbce_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"-a_3](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a9098f1754f21ebdb169710a81771238_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"a_2:\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2789190f1df15f5bd570b643d9bb29f3_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"2a_2+a_3](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5d375653cd224859cfb1172eff34b13a_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"2a_2=1-1\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cd6833a5f5007dec00e1b7a1c0820bd9_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"2a_2=0\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-aa265a6ea06995349079b84bfae9d627_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\bm{a_2=0}\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0d26904a10ba1c4d37589b41962c6b9b_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"a_1:\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c80696de686104689a20cb70c0033830_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"a_1](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9506e180ee4e8b7a69fa509b823fdcca_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"a_1=3](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f27368cbdc2111d5e30c1c29c5da8f95_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\vv{\\text{x}}=](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-80aba06b670bf9eedd4074be0750c3d0_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\vv{\\text{x}}=](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0cad8a3d5bdbe0461d347a8a3f21f794_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\vv{\\mathbf{x}}\\bm{=](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8ccdc9d2a3852c38c4442d0b601b6644_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\vv{\\text{u}}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0558431e1c2e3040ed06e8bd04be0d3b_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\vv{\\text{v}}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8f5713006a9840d2d71efbe7b540d21a_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\cfrac{2}{1}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fc4cadf576dfcd515bba9e31c113c317_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\vv{\\text{w}}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-97cea7925862c08ac4cf5b4963c0187b_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\cfrac{2}{-3}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ccc5afad1474f92824813625a0f04242_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\cfrac{1}{-3}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f818eb5ae0825dd43290331519599c21_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\vv{\\text{v}}=](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ca9417b2ef9db0db6d78c0af39dde0b0_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\vv{\\text{w}}=](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-69433589474e50574aa5d9dcbd188b28_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\vv{\\text{x}}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0c010556cb8d46303e7253102ef28e47_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\vv{\\text{u}}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-88611544e069c7a373363f2f708dcd8c_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"a_1\\begin{pmatrix}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1b5da9716a3ae4f55bf8997927615f71_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\begin{pmatrix}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ea9db980d051c022dc56036cd96b054f_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\begin{pmatrix}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8e0fc02c135530814884b62685cc22b4_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\left.](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1ea3ca998fc7d9d9b2cf42d43a5bf0a4_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\left(](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c808441bc71bd26e333ebe2169b738ca_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\left(\\begin{array}{ccc|c}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-941792a2de155bc284b14e34dc561418_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\left(\\begin{array}{ccc|c}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7105de2fa579f40818bccc2df48961ab_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\left.](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bfd5b2d564f66cd225c1a5987241ba14_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"-3a_3](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-667fa5894272768e2e53f618a9752611_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"a_3](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9b4234a97996e589d5d34b629a19bd0c_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"3a_2=6\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-45078dcd57cac62db8e98338a22dd939_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"a_2=\\cfrac{6}{3}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0580c5be6b3c77cbd727adef2f128343_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"a_1](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1db29b41da87b5381698bd496ad4887e_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"a_1](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b02c7b15b3b51ac99fe4d36f6f084283_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"a_1](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d561c23489e6cc9b0680dbe0601babbf_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"a_1=1](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a770689380f00a654857e19b755a1dd6_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\vv{\\text{x}}=](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7115a844fd089e1dd6d17e0148dfe115_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\vv{\\mathbf{x}}\\bm{=](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5042840d8d9f0844c2f122aa96f850a6_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\vv{\\text{x}}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e87fcd25b965f26fff25c11b2c341f5e_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\vv{\\text{u}}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f4d916d955d40ff456668de002eebc5e_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\vv{\\text{x}}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-910bbc90f3e6b9fb743fe6e64dbb83d9_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"a_1\\begin{pmatrix}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6c8f5b0f83b3724f96bea45f4f8c6770_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\begin{pmatrix}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-66170c955f7d70bd675d864ad5f346a7_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\begin{pmatrix}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e2a60cf7c088c8640c23e6c86ed1c00d_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\left.](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-acdcf13a945bca16684be340d27e3523_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\left(](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e49ae26fc68a865214bd9b6146b7aa99_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\left(\\begin{array}{ccc|c}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e4c56b420242d0abe6f77b3ed1a60e54_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\left.](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-03461ed9ebda463d2f0a1bb6894657be_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"a_3](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0abc9e623042fbe70cd55d4084945584_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"-9a_2-2a_3](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6bb0b04bcb9cce3edf56853f8b035b69_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"-9a_2+8](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c798313fd76263436ded44def0ac8ba5_l3.png\" "\\"Rendered")
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