MATH 2211 Midterm: Exam3210Spr11
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Specify whether the matrix has an inverse without trying to compute the inverse. 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. (b) let a = 1 (a 1)(a2 4) a a. Determine those values of a for which a is invertible. Let a = a b c d e f g h i and assume that det(a) = 2. 2 a 1), det((2a)3), det(3(at ) 1), and det a b g h d e c + 2a i + 2g f + 2d. Find all solutions to the system using cramer"s rule. Find the inverse of the matrix below using the inverse formula. Find the volume of the parallelepiped t(s) where s is the parallelepiped given in part (a).
