MATH 2211 Midterm: Exam3210Sample5Ans
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Specify whether the matrix has an inverse without trying to compute the inverse. We calculate the determinant across the 2nd rows and 3rd column. (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) Since we have the determinant is 0, the matrix is not invertible. The properties of determinants (a) an n n matrix a is called skew-symmetric if at = a. Show that if a is skew-symmetric and n is an odd positive integer, then a is not invertible. Answer det(at) = det( a) det(a) = det( a) det(a) = ( 1)ndet(a) det(a) = det(a). So, we get det(a) = 0 which implies that a is not invertible. Note that a means that every row of a is multiplied by -1. (b) let a = . Determine those values of for which a is invertible. By imt, a is invertible if and only if det(a) = det(b) = 0. Let a = a b c d e f g h i and assume that det(a) = 10.
