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Suppose T: $R^2->R^2$ is the linear transformation associated to the matrix

A= \begin{bmatrix}\frac{{\sqrt2}}{2}&\frac{{\sqrt2}}{2}\\\frac{-{\sqrt2}}{2}&\frac{{\sqrt2}}{2}\\\end{bmatrix}

The unit square U is the square whose vertices are the points (0, 0), (1, 0), (1, 1), and (0, 1) in the plane $R^2$. Draw the image of U under the linear transformation T. Be sure to include the coordinate axis in your graph.

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    What are your thoughts? What's the result if you multiply the matrix with either of these vectors? – 2017-02-18
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    Would you have to find the image based off the matrix first? – 2017-02-18
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    Calculating $A\begin{pmatrix} 1 \\0 \end{pmatrix}$ is precisely finding the image of $\begin{pmatrix} 1 \\0 \end{pmatrix}$ under $A$. – 2017-02-18
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    It's still not clear to me how I would find the image of the points under A. – 2017-02-18
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    Multiply each of them by $A$, of course. – 2017-02-18
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    So, would you just multiply each point by A and then plot it or is there more to this? – 2017-02-18
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    That's precisely the excercise. – 2017-02-19
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    $A$ just rotates $U$ by $45^o$ about the origin. Is this a homework problem? – 2017-03-15

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