- #1
Niles
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Homework Statement
A linear transformation L : R2 -> R3 is defined by:
[tex]L({\bf{x}}) = \left( {x_2 ,x_1 + x_2 ,x_1 - x_2 } \right)^T[/tex]
I wish to find the matrix representation of L with respect to the orderes bases [u1, u2] and [b1, b2, b3], where
u1 = (1,2)
u2 = (3,1)
andb1 = (1,0,0)
b2 = (1,1,0)
b3 = (1,1,1).
The Attempt at a Solution
Ok, I what I want to do is to find the matrix representation of L with respect to U and the standard basis E (I call this matrix A), and then find the matrix representation of L with respect to E and B (I call this matrix X). Then I will multiply these two matrices:
[tex]\[
A = \left( {\begin{array}{*{20}c}
2 \hfill & 1 \hfill \\
3 \hfill & 4 \hfill \\
{ - 1} \hfill & 2 \hfill \\
\end{array}} \right)
\]
[/tex]
and
[tex]\[
X = \left( {\begin{array}{*{20}c}
{ - 1} \hfill & 0 \hfill \\
0 \hfill & 2 \hfill \\
1 \hfill & { - 1} \hfill \\
\end{array}} \right)
\]
[/tex].
I believe that the matrix I am being asked for is X*A. But this won't work because of the dimensions. What am I missing here?Niles.