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Math Help - linear transformation ad standard basis

  1. #1
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    linear transformation ad standard basis

    Let T: R^3-->R^3 be a linear transformation defined by T(x, y, z)=(2x+y, x+2z, x+y+z). Find the matrix A of T relative to the standard basis of R^3.

    I know what the standard matrix is of R^3 I'm just confused by the 'A of T'. Does that mean that I take the coefficient matrix of T combined with the standard basis of R^3 and row reduce it as if I was finding change-of-coordinate vectors?

    Thank you to anyone who can set me on the right path.
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  2. #2
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    don't know what you mean exactly but the procedure is quite simple:

    find T(1,0,0),T(0,1,0),T(0,0,1) once you got the images, then transpose each vector and you'll get the matrix.
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  3. #3
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    what answer would you get? I just want to make sure that I am doing this right. Thanks for your help.
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  4. #4
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    no time now for giving you the answer but, first we have T(1,0,0)=(2,1,1).

    so the first column of your matrix is (2,1,1)^t. Do the same for the others and you'll get the matrix which represents your transformation.
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