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## Homework Statement

Find the matrix of the transformation:[tex]T: R^{2} \rightarrow R^{2x2}[/tex]

[tex]

\[

T(a,b) =

\left[ {\begin{array}{cc}

a & 0 \\

0 & b \\

\end{array} } \right]

\][/tex]

## Homework Equations

## The Attempt at a Solution

I choose the standard bases for [tex]R^{2}[/tex] and [tex]R^{2x2}[/tex] and call them b and b' respectively.

[tex]T(1,0) = 1e_{1} + 0e_{2} + 0e_{3} + 0e_{4}[/tex]

[tex]T(0,1) = 0e_{1} + 0e_{2} + 0e_{3} + 1e_{4}[/tex]

This gives me a matrix of

[tex]

\[

\left[ {\begin{array}{cc}

1 & 0 \\

0 & 0 \\

0 & 0 \\

0 & 1 \\

\end{array} } \right]

\][/tex]

However, this doesn't work when I multiply by the column vector (a,b). I get a column vector of (a, 0, 0, b) instead of a 2x2 matrix. What's going on?