Exercise 2

This problem concerns the identification of matrix transformations, about which more will be said in the next section.

1. Check that the following function $T:\real^3\to\real^2$ is a matrix transformation by finding a matrix $A$ such that $T(\xvec) = A\xvec$. $$T\left(\threevec{x_1}{x_2}{x_3}\right) = \left[\begin{array}{c} 3x_1 - x_2 + 4x_3 \\ 5x_2 - x_3 \\ \end{array}\right]$$.

2. Explain why $$T\left(\threevec{x_1}{x_2}{x_3}\right) = \left[\begin{array}{c} 3x_1^4 - x_2 + 4x_3 \\ 5x_2 - x_3 \\ \end{array}\right]$$ is not a matrix transformation.