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Math Help - Show that A is non-singular

  1. #1
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    Show that A is non-singular

    Suppose that the nxn matrix A is column equivalent to the identity In and that E1, E2,....,Ek are the elementary matrices which perform the corresponding column operations (in order) to transform A to In. Show that A is non-singular and find A^-1 in terms of the E's.

    I am confused with the difference betwen row equivalent and column equivalent, and what is E's?
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    Quote Originally Posted by 450081592 View Post
    Suppose that the nxn matrix A is column equivalent to the identity In and that E1, E2,....,Ek are the elementary matrices which perform the corresponding column operations (in order) to transform A to In. Show that A is non-singular and find A^-1 in terms of the E's.

    I am confused with the difference betwen row equivalent and column equivalent, and what is E's?

    Row equiv. = product of the matrix by elementary matrices from the left, column equiv. = product from the right. As simple as that, and thus:

    We're given that AE_1\cdot...\cdot E_k=I_n\,\Longrightarrow\,A^{-1}=E_1\cdot ...\cdot E_k ...

    Tonio
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    Quote Originally Posted by tonio View Post
    Row equiv. = product of the matrix by elementary matrices from the left, column equiv. = product from the right. As simple as that, and thus:

    We're given that AE_1\cdot...\cdot E_k=I_n\,\Longrightarrow\,A^{-1}=E_1\cdot ...\cdot E_k ...

    Tonio
    so is that it? The proof is already in the question?
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