- #1

- 643

- 1

[tex]

T \left[ \begin{array}{cccc} 2 \\ 2 \end{array} \right] = \left[ \begin{array}{cccc} 1 \\ 2 \end{array} \right]

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[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?