# linear transformation ad standard basis

• Oct 22nd 2009, 04:45 PM
arizona11
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.
• Oct 22nd 2009, 05:02 PM
Krizalid
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.
• Oct 22nd 2009, 11:42 PM
arizona11
what answer would you get? I just want to make sure that I am doing this right. Thanks for your help.
• Oct 23rd 2009, 06:12 AM
Krizalid
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.