Exercise5

Suppose \(T:\real^3\to\real^2\) is a matrix transformation with \(T(\evec_j) = \vvec_j\) where \(\vvec_1\text{,}\) \(\vvec_2\text{,}\) and \(\vvec_3\) are as shown in FigureĀ 6.

<<SVG image is unavailable, or your browser cannot render it>>

Figure2.5.6The vectors \(T(\evec_j)=\vvec_j\text{.}\)

  1. Sketch the vector \(T\left(\threevec{2}{1}{2}\right)\text{.}\)

  2. What is the vector \(T\left(\threevec{0}{1}{0}\right)\text{?}\)

  3. Find all the vectors \(\xvec\) such that \(T(\xvec) = \zerovec\text{.}\)

in-context