MATH 1553 Quiz: MATH 1553 GT 11 03 Quiz a
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[2 points each] compute the determinants of the following matrices. [hint: none require extensive calculations. : 1. For this matrix, it is probably easiest to use the formula for the determinant of a 3 3 matrix: det 1. Here it is easiest to use cofactor expansion along the third column, then the. 0 3 2 = 6 det 2 4. This is an upper-triangular matrix, so its determinant is the product of the diagonal entries: The second column is a multiple of the rst. Hence the columns are linearly dependent, so the matrix is not invertible, so its determinant is zero. d e f. , assuming det a b c g h i = 1. d e f (notice the rst matrix is cubed. ) is obtained from a b c g h i by do- d e f ing one row swap, multiplying one row by 2, and doing one row replacement (not necessarily in that order).
