DE6spring08

# DE6spring08 - Practice Problems MTH 2201 1 Let A = 3 1 5 2...

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Practice Problems MTH 2201 4/1/2008 1. Let A = " 3 1 5 2 # , B = " 2 - 3 4 4 # . (a) Find A - 1 , B - 1 . Verify ( AB ) - 1 = B - 1 A - 1 . (b) Find a matrix that satisﬁes the equation AX + B = BA . (c) Find A - 2 and then ﬁnd p ( A ) for p ( x ) = x 2 - 2 x + 1 . 2. If ( I + 2 A ) - 1 = " - 1 2 4 5 # ﬁnd A . 3. Find all values of c , if any, for which A = " c 1 c c # is invertible. 4. Find an matrices E 1 , E 2 such that E 1 A = B and E 2 C = A . Use the matrices given in Q.1. 5. Find the inverse of the given matrices: A = 3 4 - 1 1 0 3 2 5 - 4 , B = 1 0 1 0 1 1 1 1 0 , C = 1 2 3 0 2 3 0 0 3 . 1

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6. Consider the matrix A = 1 0 - 2 0 1 0 0 0 2 . (a) Find elementary matrices E 1 and E 2 such that E 1 E 2 A = I . (b) Write A - 1 as a product of two elementary matrices. (c) A as a product of two elementary matrices. 7. Solve the two systems at once by row reduction:
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DE6spring08 - Practice Problems MTH 2201 1 Let A = 3 1 5 2...

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