1 2 2a 3c b c 2d 3 f e f 2 g 3i h i 1 2 abc def

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Unformatted text preview: 2). By Cramer’s Rule it is x1 = 1) + 3(0) = 2. 2a − 3c b c 2d − 3 f e f 2 g − 3i h i /( − 1) = − 2 abc def ghi +3 cbc fef ihi = − 2( − Part II 13. a) We have A X 2 = (A X )⊤(A X ) = X ⊤ A⊤A X = X ⊤X = X A− 1 = A⊤ to say that A⊤A = I . 1 2 , where we used b) Let λ be an eigenvalue of A and X be an eigenvector for it. Then, by a), 0). |λ | X = A X = X , so that |λ | = 1 (since X c) Assume A is symmetric. Then A = A⊤, so A2 = I ⇔ A− 1 = A ⇔ A− 1 = A⊤. 14. a) The description of...
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