WeBWorK Standalone Renderer

Each of the following six matrices defines a linear transformation $T_i : \mathbb{R}^3 \to \mathbb{R}^3$ by $T_i(\mathbf{x}) = A_i \mathbf{x}$ .

$\displaystyle{ A_1 = {\left[\begin{array}{ccc} 2 &-2 &0\cr 0 &0 &0\cr 0 &0 &3 \end{array}\right]} }$ , $\displaystyle{ A_2 = {\left[\begin{array}{ccc} 2 &-2 &0\cr 0 &0 &1\cr 0 &0 &0 \end{array}\right]} }$ , $\displaystyle{ A_3 = {\left[\begin{array}{ccc} 3 &0 &-3\cr 0 &2 &0\cr 0 &0 &0 \end{array}\right]} }$

$\displaystyle{ A_4 = {\left[\begin{array}{ccc} 1 &1 &0\cr 0 &2 &0\cr 0 &0 &0 \end{array}\right]} }$ , $\displaystyle{ A_5 = {\left[\begin{array}{ccc} 1 &0 &0\cr -2 &0 &0\cr 3 &0 &0 \end{array}\right]} }$ , $\displaystyle{ A_6 = {\left[\begin{array}{ccc} 0 &0 &2\cr 0 &-3 &0\cr 1 &0 &0 \end{array}\right]} }$

Using the drop down menus below each image, match each matrix with the picture of the kernel and image of its linear transformation. The kernel and image are colored red. All red lines and planes have infinite extent, and a shaded cube represents all points in $\mathbb{R}^3$ .

In order to get credit for this problem all answers must be correct.