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November 8th, 2018, 02:28 AM   #1
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Geometric representation of matrix transformation

I want to sketch the 2-vector $\displaystyle \textbf{u}=\left( \begin{array}{c}
3 \end{array} \right)$ and its image under the matrix transformation $\displaystyle f: R^2\rightarrow R^3$ defined by $\displaystyle f(u)=\left( \begin{array}{cc}
1 & 0\\
1 & -1\\
0 & 1 \end{array} \right)\textbf{u}.$ Can I sketch both of $\displaystyle \textbf{u}$ and $\displaystyle f(\textbf{u})$ on the three-dimensional space together as follow? Why? Or sketch them separately with $\displaystyle \textbf{u}$ on the two-dimensional space and $\displaystyle f(\textbf{u})$ on the three-dimensional space? Thank you.
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November 14th, 2018, 05:36 AM   #2
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You can sketch any plane, and the vectors in it, on a three dimensional space.
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