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Math225_Q3_soln

Math225_Q3_soln - Math 225 Quiz 3 Solutions 1 2 3 0 4 0 7 2...

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Math 225: Quiz 3 Solutions 1. Consider the matrix A = 1 - 2 3 0 4 0 7 - 2 0 1 3 4 1 5 - 2 0 . Use cofactor expansion to find the determinant. SOLUTION: We choose a row or column to expand by. Since the fourth column of A has the most zeros, we will expand by it. (Note you could have chosen a different row/column and get the same solution). A = - (0)det 4 0 7 0 1 3 1 5 - 2 + ( - 2)det 1 - 2 3 0 1 3 1 5 - 2 - (4)det 1 - 2 3 4 0 7 1 5 - 2 + (0)det 1 - 2 3 4 0 7 0 1 3 = - 2 · det 1 - 2 3 0 1 3 1 5 - 2 - 4 · det 1 - 2 3 4 0 7 1 5 - 2 = - 2 1 · det 1 3 5 - 2 + 1 · det - 2 3 1 3 - 4 - 4 · det - 2 3 5 - 2 - 7 · det 1 - 2 1 5 (1) = - 2[(1)( - 2) - (3)(5) + ( - 2)(3) - (1)(3)] - 4[ - 4(( - 2)( - 2) - (3)(5)) - 7((1)(5) - ( - 2)(1))] = - 2[ - 2 - 15 - 6 - 3] - 4[ - 4(4 - 15) - 7(5 + 2)] = - 2( - 26) - 4(44 - 49) = 52 + 20 = 72 In (1) we again used cofactor expansion to find the determinant of both resulting matrices;
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