- #1
crashh
- 1
- 0
Homework Statement
The problem states that we have L as the linear transformation as:
\begin{align*}
A=
\left(
\begin{array}{ccc}
2 & 0 & 1 \\
-2 & 3 & 2 \\
4 & 1 & 5
\end{array}
\right)
\end{align*}
And when given another linear transformation T as:
\begin{align*}
B=
\left(
\begin{array}{ccc}
-3 & 1 & 0 \\
2 & 0 & 1 \\
0 & -1 & 3
\end{array}
\right)
\end{align*}
Then find the matrix representation of T ο L with respect to E(which is the standard basis, as are both transformations).
T ο L is the composition of T and L.
Homework Equations
I assumed you could just multiply the two matrices togeather, as they share the same basis, thus getting the composition of the two lineartransformations?
The Attempt at a Solution
\begin{align*}
T&=B=
\left(
\begin{array}{ccc}
-3 & 1 & 0 \\
2 & 0 & 1 \\
0 & -1 & 3
\end{array}
\right)\\
L&=A=
\left(
\begin{array}{ccc}
2 & 0 & 1 \\
-2 & 3 & 2 \\
4 & 1 & 5
\end{array}
\right)\\
\end{align*}
\begin{align*}
BA&=
\left(
\begin{array}{ccc}
-3 & 1 & 0 \\
2 & 0 & 1 \\
0 & -1 & 3
\end{array}
\right)
\left(
\begin{array}{ccc}
2 & 0 & 1 \\
-2 & 3 & 2 \\
4 & 1 & 5
\end{array}
\right)\\
&=
\left(
\begin{array}{ccc}
-8 & 3 & -1 \\
8 & 1 & 7 \\
14 & 0 & 13
\end{array}
\right)
\end{align*}
Or is this completely wrong?