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Math Help - Help with Intro Lin. Alg. proof please?

  1. #1
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    Help with Intro Lin. Alg. proof please?

    I've been brushing up on some linear algebra this summer, and came across this problem in a practice book. Any help on this?

    Let A be an m x n matrix. Prove that if c is any nonzero scalar, then rank(cA) = rank(A).
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  2. #2
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    Quote Originally Posted by paupsers View Post
    I've been brushing up on some linear algebra this summer, and came across this problem in a practice book. Any help on this?

    Let A be an m x n matrix. Prove that if c is any nonzero scalar, then rank(cA) = rank(A).
    Any m by n matrix is a linear transformation from R^m to R^n and, if its rank is k, its image is k dimensional subspace of R^n. If you know the image of A, what can you say about the image of cA? In particular, if Ax= y, what is (cA)x?
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  3. #3
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    Another way to thin about it is that the rank of a matrix is the number of linearly independent rows (or columns, which ever is smaller) there are in a matrix. So what happens when you multiply everything by some scalar?
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