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quiz3 - 4 Find the inverse of the following n × n matrix A...

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Math 54 Wednesday, February 11 Quiz 3 1. Suppose T and U are linear transformations from R n to R n such that T ( U ( x )) = x for all x R n . Is that true that U ( T ( x )) = x for all x R n . Explain. 2. What is the rank of a 4 × 5 matrix whose null space is three-dimensional? 3. Let A be a matrix and B be an echelon form of A : A = - 3 9 - 2 - 7 2 - 6 4 8 3 - 9 - 2 2 1 - 3 6 9 0 0 4 5 0 0 0 0 (a) Find a basis for Col A . (b) Find a basis for Nul A . 4. Find the inverse of the following
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Unformatted text preview: . 4. Find the inverse of the following n × n matrix: A = 1 0 0 ... 1 2 0 ... 1 2 3 ... . . . . . . . . . 1 2 3 ... n . [ Hint : Use the algorithm for the case 3 × 3 or 4 × 4, guess the answer for the n × n matrix and prove it is indeed A-1 .] 1...
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