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04win-m2

04win-m2 - MATH 51 MIDTERM 2 1 Find the inverse of the...

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MATH 51 MIDTERM 2 February 26, 2004 1. Find the inverse of the matrix A = 1 - 1 1 - 1 1 1 1 1 - 1 . 2. Suppose A and B are 3x3 matrices, and that det( A ) = 5 and det( B ) = - 2. (a) Find det( AB ). (b) Find det( A - 1 ). (c) Find det(2 A ). 3. Let A = 0 - 1 2 3 . (a) Find the eigenvalues of A . (b) Find the eigenvalues of A 10 . (c) The matrix A = 2 1 1 1 3 - 2 1 - 2 3 has the number 3 as one of its eigenvalues. Find an eigenvector v that has 3 as its associated eigenvalue. 4. Let T : R 2 R 2 be the linear transformation deﬁned by: T x y = x + y - 2 x + 4 y . (a). Find the matrix A that represents the linear transformation T with respect to the standard basis S = { e 1 , e 2 } . (b). Consider the basis B = { v 1 , v 2 } given by: v 1 = 1 2 , v 2 = 3 7 . Find the change of basis matrix C for the basis B . That is, ﬁnd the matrix C such that v = C [ v ] B for all vectors v .

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04win-m2 - MATH 51 MIDTERM 2 1 Find the inverse of the...

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