# Linear transformation problem

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• Jul 17th 2008, 12:41 PM
tttcomrader
Linear transformation problem
Suppose that the linear transformation T maps $\displaystyle \left[ \begin{bmatrix}1\\0 \end{bmatrix} \right]$ to $\displaystyle \left[ \begin{bmatrix}2\\5 \end{bmatrix} \right]$ and $\displaystyle \left[ \begin{bmatrix}0\\1 \end{bmatrix} \right]$ to $\displaystyle \left[ \begin{bmatrix}-1\\6 \end{bmatrix} \right]$

Find T($\displaystyle \left[ \begin{bmatrix}x_1\\x_2 \end{bmatrix} \right]$)
• Jul 17th 2008, 01:05 PM
TKHunny
Unless I'm asleep and don't know it (which certainly could be the case), it's an eyeball problem.

$\displaystyle [2x_{1}-x_{2},5x_{1}+6x_{2}]^{T}$
• Jul 17th 2008, 01:09 PM
bobak
Quote:

Originally Posted by tttcomrader
Suppose that the linear transformation T maps $\displaystyle \left[ \begin{bmatrix}1\\0 \end{bmatrix} \right]$ to $\displaystyle \left[ \begin{bmatrix}2\\5 \end{bmatrix} \right]$ and $\displaystyle \left[ \begin{bmatrix}0\\1 \end{bmatrix} \right]$ to $\displaystyle \left[ \begin{bmatrix}-1\\6 \end{bmatrix} \right]$

Find T($\displaystyle \left[ \begin{bmatrix}x_1\\x_2 \end{bmatrix} \right]$)

Your told that the transformation is linear, you're given the images of the unit vectors i and j so can you determine a the 2by2 matrix to represent this transformation ? it quiet easy if you are unsure remember that the image of the i vectors tells you that $\displaystyle \left(\begin{array}{cc}a & b \\c & d\end{array}\right) \times \left(\begin{array}{c}1 \\0\end{array}\right) = \left(\begin{array}{c}2 \\5\end{array}\right)$ you should easily be able to determine a, b c, and d.

then $\displaystyle T\left(\begin{array}{c}x_1 \\x_2\end{array}\right) = \left(\begin{array}{cc}a & b \\c & d\end{array}\right) \times \left(\begin{array}{c}x_1 \\x_2\end{array}\right)$

Bobak