MATH 2211 Midterm: Exam3210Spr11Ans
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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. Since we have the determinant is not 0, the matrix is 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 = . 1 (a 1)(a2 4) a a. Determine those values of a for which a is invertible. Notice that the given matrix is a triangular matrix. By imt, a is invertible if and only if det(a) = (1)(a 1)2(a2 4)a = 0.
