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l.ct A be an 11 x 11 matrix and b1 , denote the (k

Elementary Linear Algebra: A Matrix Approach | 2nd Edition | ISBN: 9780131871410 | Authors: Lawrence E. Spence ISBN: 9780131871410 187

Solution for problem 82 Chapter 3.2

Elementary Linear Algebra: A Matrix Approach | 2nd Edition

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Elementary Linear Algebra: A Matrix Approach | 2nd Edition | ISBN: 9780131871410 | Authors: Lawrence E. Spence

Elementary Linear Algebra: A Matrix Approach | 2nd Edition

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Problem 82

l.ct A be an 11 x 11 matrix and b1 , denote the (k .j)cofactor of A. (a) Pro'e that if P is the matrix obtained from A by replac1ng column k by e1 . then det P = bi.J . (b) Show th:ll for each j , we have /lim: Apply Cramer's rule to Ax = e 1. (c) Deduce that1f B is the" x 11 matrix who;e (i.j)-entry is b, 1 thenA8 = detA)/ . This matrix 8 is called the classict1/ adjoim of A. I (d) Sho\\ that if detA :f= 0. then A- 1 = --B.

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Chapter 3.2, Problem 82 is Solved
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Textbook: Elementary Linear Algebra: A Matrix Approach
Edition: 2
Author: Lawrence E. Spence
ISBN: 9780131871410

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l.ct A be an 11 x 11 matrix and b1 , denote the (k