Let A be a 3 3 matrix. Show that if A is the matrix obtained from A using any of the

Chapter 6, Problem 6.4.10

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Let A be a 3 3 matrix. Show that if A is the matrix obtained from A using any of the operations (E1) (E2), (E1) (E3), or (E2) (E3), then det A = det A. has x1 = 1 D det b1 a12 a13 b2 a22 a23 b3 a32 a33 D1 D , x2 = 1 D det a11 b1 a13 a21 b2 a23 a31 b3 a33 D2 D , and x3 = 1 D det a11 a12 b1 a21 a22 b2 a31 a32 b3 D3 D , where D = det a11 a12 a13 a21 a22 a23 a31 a32 a33

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