Unformatted text preview: P , then M is row equivalent to P . 4. (8 points) Prove the following. If X and Y are n × n matrices and X Y = I then X is invertible and X1 = Y . 5. (9 points) Let A be an n × n matrix. (a) Deﬁne what it means to say that A is nonsingular . (b) Prove the theorem that states that if A is nonsingular, then its inverse is unique. 6. (8 points) A matrix W is called skewsymmetric if W T =W . Prove that if B is a square matrix, then BB T is skewsymmetric. 1...
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 Spring '09
 RUDYAK
 Linear Algebra, Matrices, 2W, Invertible matrix, 3W

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