CPM Homework Help : PC3 Problem 11-119

Let $M = \left[ \begin{array} { l l } { 1 } & { 2 } \\ { 3 } & { 0 } \end{array} \right]$ and $N = \left[ \begin{array} { l l } { a } & { 4 } \\ { c } & { d } \end{array} \right]$ . Determine the values of $a$ , $c$ , and $d$ if $MN = NM$ .

Step 1:

$\begin{bmatrix}1&2\\3&0\end{bmatrix} \begin{bmatrix}a&4\\c&d\end{bmatrix}= \begin{bmatrix}a&4\\c&d\end{bmatrix} \begin{bmatrix}1&2\\3&0\end{bmatrix}$

Step 2:

$\begin{bmatrix}a+2c&1+2d\\3a&12\end{bmatrix}=\begin{bmatrix}a+12&2a\\c+3d&2c\end{bmatrix}$