| What is the matrix M for the equations 3x+2y=9 and 4x+5y=5? | M=\begin{pmatrix}3&2\\4&5\end{pmatrix} |
| How do you calculate \det M for M=\begin{pmatrix}3&2\\4&5\end{pmatrix}? | \det M=(3)(5)-(2)(4)=7 |
| What is M^{-1} for M=\begin{pmatrix}3&2\\4&5\end{pmatrix}? | M^{-1}=\frac17\begin{pmatrix}5&-2\\-4&3\end{pmatrix} |
| How do you find \begin{pmatrix}x\\y\end{pmatrix} using the inverse matrix for 3x+2y=9 and 4x+5y=5? | \begin{pmatrix}x\\y\end{pmatrix}=\frac17\begin{pmatrix}5&-2\\-4&3\end{pmatrix}\begin{pmatrix}9\\5\end{pmatrix}=\frac17\begin{pmatrix}35\\-21\end{pmatrix}=\begin{pmatrix}5\\-3\end{pmatrix} |
| What is the solution for x and y in the system 3x+2y=9 and 4x+5y=5? | x=5, y=-3 |