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Unformatted text preview: x 1 + (1i ) x 2 = 0 —————— 6. Solve proofwriting exercises 1,3 in chapter 3 7. Solve proofwriting exercises 1,3,4 from chapter 12. 1 8. Find two examples of 2 × 2 matrices with the property that A 2 = 0 but A 6 = 0. 9. For which values of k does the following system have a solution: x 1 + x 2 + x 3 + x 4 = 1 x 1 + x 3 = 1 x 2 + x 4 k 10. for which values of ( a, b, c ) does the following system have a solution? 3 x 1x 2 +2 x 3 = a 2 x 1 + x 2 + x 3 = b x 13 x 2 = c 11. Suppose A is a 2 × 1 matrix and B is a 1 × 2 matrix. Show that AB is not invertible. 12. Recall that a square matrix is upper triangular if A ij = 0 for i > j . Show that a square upper triangular matrix is invertible if and only if each of its diagonal elements are nonzero. 2...
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 Spring '10
 smith
 Math, Linear Algebra, Algebra, Triangular matrix, Calculational Exercises

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