A6S - ASSIGNMENT 6 Solutions Let n be odd, and T : R n R n...

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Unformatted text preview: ASSIGNMENT 6 Solutions Let n be odd, and T : R n R n be the linear transformation given by T : x 1 x 2 x 3 . . . x n- 1 x n 7 x 1 + x 2 x 2 + x 3 x 3 + x 4 . . . x n- 1 + x n x n + x 1 1. [4 marks] Find the standard matrix, kernel and range of T . Let e i denote the i th column of the n n identity matrix. Then the standard matrix of T is A = T ( e 1 ) T ( e n ) = 1 1 1 1 1 . . . . . . . . . . . . . . . . . . . . . 1 1 1 1 1 1 . This matrix is invertible. Taking the determinant along the 1 st column, we get det A = det 1 1 1 . . . . . . . . . . . . . . . . . . 1 1 1 1 1 + (- 1) n +1 det 1 1 1 ....
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This note was uploaded on 04/07/2010 for the course MATH 136 taught by Professor All during the Fall '08 term at Waterloo.

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A6S - ASSIGNMENT 6 Solutions Let n be odd, and T : R n R n...

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