- #1
notmuch
- 16
- 0
Hello. I am given the following:
T([1,2,-3]) = [1,0,4,2]
T([3,5,2]) = [-8,3,0,1]
T([-2,-3,-4]) = [0,2,-1,0]
And of course I know that:
T(x) = Ax
and I want to find the matrix A.
So, from the individual equations, I construct:
A[1, 2, -3] = [1, 0, 4, 2] (please forgive, these are actually col. vectors)
I do something similar for the other two, and come up with the equation below. I can solve this equation to obtain (the correct) matrix A, but I can't seem to find an explanation for why it is possible to throw it all together into "combined matrices." Could anyone help? Thanks!
[tex]
A\begin{pmatrix}
1 & 3 & -2\\
2 & 5 & -3\\
-3 & 2 & -4\end{pmatrix} =
\begin{pmatrix}
1 & -8 & 0\\
0 & 3 & 2\\
4 & 0 & -1\\
2 & 1 & 0\end{pmatrix}
[/tex]
T([1,2,-3]) = [1,0,4,2]
T([3,5,2]) = [-8,3,0,1]
T([-2,-3,-4]) = [0,2,-1,0]
And of course I know that:
T(x) = Ax
and I want to find the matrix A.
So, from the individual equations, I construct:
A[1, 2, -3] = [1, 0, 4, 2] (please forgive, these are actually col. vectors)
I do something similar for the other two, and come up with the equation below. I can solve this equation to obtain (the correct) matrix A, but I can't seem to find an explanation for why it is possible to throw it all together into "combined matrices." Could anyone help? Thanks!
[tex]
A\begin{pmatrix}
1 & 3 & -2\\
2 & 5 & -3\\
-3 & 2 & -4\end{pmatrix} =
\begin{pmatrix}
1 & -8 & 0\\
0 & 3 & 2\\
4 & 0 & -1\\
2 & 1 & 0\end{pmatrix}
[/tex]