- #1
Lancelot59
- 646
- 1
I'm given the following linear transformations:
[tex]
T \left[ \begin{array}{cccc} 2 \\ 2 \end{array} \right] = \left[ \begin{array}{cccc} 1 \\ 2 \end{array} \right]
[/tex]
[tex]
T \left[ \begin{array}{cccc} -4 \\ 0 \end{array} \right] = \left[ \begin{array}{cccc} -5 \\ 1 \end{array} \right]
[/tex]
I need to find:
[tex]
T \left[ \begin{array}{cccc} -2 \\ 3 \end{array} \right] = ?
[/tex]
I solved prior problems by just reverse engineering it. That method seemed to fail here.
I came up with the following
[tex]
T \left[ \begin{array}{cccc} x_{1} \\ x_{2} \end{array} \right] = \left[ \begin{array}{cccc} x_{1}-1 \\ \frac{x_{2}}{3}+1 \end{array} \right]
[/tex]
And it worked for both of the given cases, but it didn't for the unknown.
I got [tex]T \left[ \begin{array}{cccc} -3 \\ 1 \end{array} \right][/tex], and the answer is: [tex]T \left[ \begin{array}{cccc} -4 \\ 3 \end{array} \right][/tex]
So how do I go about solving this problem?
[tex]
T \left[ \begin{array}{cccc} 2 \\ 2 \end{array} \right] = \left[ \begin{array}{cccc} 1 \\ 2 \end{array} \right]
[/tex]
[tex]
T \left[ \begin{array}{cccc} -4 \\ 0 \end{array} \right] = \left[ \begin{array}{cccc} -5 \\ 1 \end{array} \right]
[/tex]
I need to find:
[tex]
T \left[ \begin{array}{cccc} -2 \\ 3 \end{array} \right] = ?
[/tex]
I solved prior problems by just reverse engineering it. That method seemed to fail here.
I came up with the following
[tex]
T \left[ \begin{array}{cccc} x_{1} \\ x_{2} \end{array} \right] = \left[ \begin{array}{cccc} x_{1}-1 \\ \frac{x_{2}}{3}+1 \end{array} \right]
[/tex]
And it worked for both of the given cases, but it didn't for the unknown.
I got [tex]T \left[ \begin{array}{cccc} -3 \\ 1 \end{array} \right][/tex], and the answer is: [tex]T \left[ \begin{array}{cccc} -4 \\ 3 \end{array} \right][/tex]
So how do I go about solving this problem?