(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let T be the linear transformation of R5 into R3 that has the matrix

A =

1 3 2 0 -1

2 6 4 6 4

1 3 2 2 1

relative to the bases [(1,1,1,1,1), (1,1,1,1,0), (1,1,0,0,0), (1,0,0,0,0), (0,0,0,0,1)] of R5 and [(1,1,1), (0,1,0), (1,0,0)] of R3. Find a basis for the range of T.

2. Relevant equations

3. The attempt at a solution

The whole ordeal with the different bases for R5 and R3 confuses me. If this was just an ordinary matrix, I'd have row reduced and gotten my basis for the range to be

{[1 2 1]^T and [0 6 2]^T.

But this isn't the correct answer. The correct answer is

[(4/3, 1, 1), (1/3, 1, 0)].

Any suggestions? Much thanks.

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# Homework Help: Basis of range of a matrix relative to some bases

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