- #1
DanielFaraday
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Homework Statement
This is a slight variation of the last problem I posted.
Write the standard matrix representation for T1T2 and use it to find [T1T2(1,-3,0)]E.
Homework Equations
[tex]
T_1\left(x_1,x_2,x_3\right)=\left(x_3,-x_1,x_3\right)
[/tex]
[tex]
T_2\left(x_1,x_2,x_3\right)=\left(x_3-x_1,x_3-2x_2-x_1,x_1-x_3\right)
[/tex]
The Attempt at a Solution
[tex]
T_1T_2=\left(x_3,-x_1,x_3\right)\cdot \left(x_3-x_1,x_3-2x_2-x_1,x_1-x_3\right)=x_1^2+2 x_1 x_2-x_1 x_3
[/tex]
[tex]
A=\left(x_1^2+2 x_1 x_2-x_1 x_3\right)\left(
\begin{array}{ccc}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{array}
\right)
[/tex]
Will A just end up being an identity matrix multiplied by the scalar that results from T1T2, or should I use a non-standard product for T1T2?
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