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 November 8th, 2018, 03:28 AM #1 Newbie   Joined: Jan 2014 Posts: 19 Thanks: 0 Geometric representation of matrix transformation I want to sketch the 2-vector $\displaystyle \textbf{u}=\left( \begin{array}{c} 2\\ 3 \end{array} \right)$ 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.
 November 14th, 2018, 06:36 AM #2 Senior Member   Joined: Mar 2015 From: New Jersey Posts: 1,628 Thanks: 119 You can sketch any plane, and the vectors in it, on a three dimensional space.

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