Hi, I'm having trouble with some questions. I did elementary linear algebra a few months ago but seeing as I've forgotten most of it I'm effectively new to this. Anyway can someone help find a basis for Im(T) the following transformation?(adsbygoogle = window.adsbygoogle || []).push({});

[tex]T:R^4 \to R^3 ,T\left( x \right) = Ax[/tex] where [tex]A = \left[ {\begin{array}{*{20}c}

1 & 2 & { - 1} & 1 \\

1 & 0 & 1 & 1 \\

2 & { - 4} & 6 & 2 \\

\end{array}} \right][/tex]

I tried applying T to each of the four vectors in the standard basis for R^4 and apply T to each in turn I got: (1,1,2), (2,0,-4), (-1,1,-4), (1,1,2). The basis for Im(T) is supposed to be {(1,1,2),(2,0,-4)} so I've done something wrong since my work shows that my answer should also have (-1,1,-4) in the basis.

Can someone explain what is required to find a basis for Im(T)?

Edit: I re-checked my textbook. Im(T) is just the column space of A isn't it?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Basis for Im(T)

**Physics Forums | Science Articles, Homework Help, Discussion**