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Linear Algebra with Applications (3rd Edition)

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110.201 Linear Algebra 5th Quiz April 22, 2005 Problem 1 Using determinant rules, find the determinant of the matrix A = 1 1 1 1 1 4 4 4 1 4 9 9 1 4 9 16 . Problem 2 True or false, with reason if true and counterexample if false: 1. If A and B are identical except in the upper-left corner, where b 11 = 2 a 11 , then det B = 2 det A . 2. The determinant of a matrix is the product of the pivots. 3. If A is invertible and B is singular, then A + B is invertible. 4. If A is invertible and B is singular, then AB is singular. Problem 3 An invertible linear map L : R n R n is called orientation preserving if det( A ) > 0, and orientation reversing otherwise.
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