WeBWorK Standalone Renderer

a. Suppose that $E_1 \left[\begin{array}{cc} 5 &-3\cr 2 &-1 \end{array}\right] = \left[\begin{array}{cc} 15 &-9\cr 2 &-1 \end{array}\right]$ . Find $E_1$ and $E_1^{-1}$ .
$E_1 =$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$ $\left]\Rule{0pt}{2.4em}{0pt}\right.$ , $E_1^{-1} =$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$ $\left]\Rule{0pt}{2.4em}{0pt}\right.$ .

b. Suppose that $E_2 \left[\begin{array}{cc} 5 &-3\cr 2 &-1 \end{array}\right] = \left[\begin{array}{cc} 2 &-1\cr 5 &-3 \end{array}\right]$ . Find $E_2$ and $E_2^{-1}$ .
$E_2 =$ , $E_2^{-1} =$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$ $\left]\Rule{0pt}{2.4em}{0pt}\right.$ .

c. Suppose that $E_3 \left[\begin{array}{cc} 5 &-3\cr 2 &-1 \end{array}\right] = \left[\begin{array}{cc} 15 &-8\cr 2 &-1 \end{array}\right]$ . Find $E_3$ and $E_3^{-1}$ .
$E_3 =$ , $E_3^{-1} =$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$ $\left]\Rule{0pt}{2.4em}{0pt}\right.$ .

d. Suppose that $E_4 \left[\begin{array}{ccc} 1 &-1 &2\cr 3 &1 &-3\cr -3 &4 &4 \end{array}\right] = \left[\begin{array}{ccc} 1 &-1 &2\cr 6 &2 &-6\cr -3 &4 &4 \end{array}\right]$ .
Find $E_4$ and $E_4^{-1}$ .
$E_4 =$ ,
$E_4^{-1} =$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$ $\left]\Rule{0pt}{3.6em}{0pt}\right.$ .

e. Suppose that $E_5 \left[\begin{array}{ccc} 1 &-1 &2\cr 3 &1 &-3\cr -3 &4 &4 \end{array}\right] = \left[\begin{array}{ccc} 1 &-1 &2\cr -3 &4 &4\cr 3 &1 &-3 \end{array}\right]$ .
Find $E_5$ and $E_5^{-1}$ .
$E_5 =$ ,
$E_5^{-1} =$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$ $\left]\Rule{0pt}{3.6em}{0pt}\right.$ .

f. Suppose that $E_6 \left[\begin{array}{ccc} 1 &-1 &2\cr 3 &1 &-3\cr -3 &4 &4 \end{array}\right] = \left[\begin{array}{ccc} 1 &-1 &2\cr 3 &1 &-3\cr 3 &-2 &16 \end{array}\right]$ .
Find $E_6$ and $E_6^{-1}$ .
$E_6 =$ ,
$E_6^{-1} =$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$ $\left]\Rule{0pt}{3.6em}{0pt}\right.$ .

You can earn partial credit on this problem.