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# Quiz5 225 - 7 1 2-1 =-14(2 If 4 × 4 matrics A and B have...

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Math. 225 - Quiz 5 October 15, 2009 Use both sides of the paper if necessary Compute the determinant of the following matrices (a) 1 0 2 - 3 7 0 1 6 - 2 Solution: Expand along row one: det 1 0 2 - 3 7 0 1 6 - 2 = 1 .det bracketleftbigg 7 0 6 - 2 bracketrightbigg +2 .dett bracketleftbigg - 3 7 1 6 bracketrightbigg = 1( - 14)+2( - 18 - 7) = - 64 . (b) 1 1 1 1 1 1 - 1 1 - 1 1 2 2 - 2 - 2 2 1 1 1 1 1 2 3 4 5 6 Solution: Since two rows are the same, the determinant is zero (c) 1 6 3 - 4 6 0 7 - 3 8 - 9 0 0 1 1 1 0 0 0 2 3 0 0 0 0 - 1 Solution: The determinant is the product of the entries on the main diag-

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Unformatted text preview: . 7 . 1 . 2 . (-1) =-14. (2) If 4 × 4 matrics A and B have det ( A ) = 10 and det ( B ) = 2 compute the determinants of (a) 2 B Solution: det (2 B ) = 2 4 det ( B ) = 32. (b) A-1 B Solution: det ( A-1 B ) = det ( B ) /det ( A ) = 2 / 10 (c) the matrix you get if you switch rows 2 and 3 in B . Solution: One row switch changes the sign of the determinant by (-1) 1 . Thus the newdeterminant is-2....
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Quiz5 225 - 7 1 2-1 =-14(2 If 4 × 4 matrics A and B have...

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