Unformatted text preview: A ) = 0 and A is not invertible. b) (3 points) Calculate the determinants of B , AB and B1 . Solution: You only need to calculate the determinant of B using a cofactor expansion. det( B ) = ± ± ± ± ± ± 0 1 2 1 2 3 2 3 5 ± ± ± ± ± ± = ± ± ± ± ± ± 1 2 1 2 311 ± ± ± ± ± ± = (1)(1) 1+2 ± ± ± ± 1 211 ± ± ± ± =1(1 + 2) =1 Above the second equality holds, because the matrix on the right of the equality is obtained from the matrix on the left by subtracting two times the second row from the third row. The other determinants can be deduced by the product rule det( A 1 A 2 ) = det( A 1 ) det( A 2 ) as follows det( AB ) = det( A ) det( B ) = (0)(1) = 0 det( I ) = det( BB1 ) = det( B ) det( B1 ) ⇒ det( B1 ) = 1 det B =1 ....
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 Spring '03
 BUSS
 Math, Linear Algebra, Algebra, Det, product rule det

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