5. Let D be a 4 x 4 matrix of the following form: a11 a12 b11...

  

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5. Let D be a 4 x 4 matrix of the following form: a11 a12 b11 b12 a21 a22 b21 b22 D = 0 0 C11 C12 0 0 C21 C22 That is D is "built up" of the four 2 2 matrices consisting of the together with a 2 x 2 matrix of 0's. Show that: det (D) = det a21 a22 C22 aijs bij and Cij coefficients, CAUTION: You might be tempted to generalize an "ad - bc" formula for a 4 x 4 matrix by taking the determinants of the four 2 2 matrices that make it up, but such a technique does not work. 5. Let D be a 4 x 4 matrix of the following form: a11 a12 b11 b12 a21 a22 b21 b22 D = 0 0 C11 C12 0 0 C21 C22 That is D is "built up" of the four 2 2 matrices consisting of the together with a 2 x 2 matrix of 0's. Show that: det (D) = det a21 a22 C22 aijs bij and Cij coefficients, CAUTION: You might be tempted to generalize an "ad - bc" formula for a 4 x 4 matrix by taking the determinants of the four 2 2 matrices that make it up, but such a technique does not work.

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To show the given equation detD det2 detA 2 2 A11 A12 022 C11 C12 C21 C22 we need to calculate ... View the full answer