##### Practice Midterm SOLUTION: #3
abbyto1607
The inverse of a matrix can by found by augmenting the original matrix with the identity matrix. For problem three, this looks like $\begin{array}{ccc} 1&1&3&|1&0&0\\ 2&2&4&|0&1&0\\ 4&1&0&|0&0&1\end{array}$ We can then reduce this to $\begin{array}{ccc} 1&0&0&|2/3&-1/2&1/3\\ 0&1&0&|-8/3&2&-1/3\\ 0&0&1&|1&-1/2&0\end{array}$. This gives the inverse matrix to be $\begin{array}{ccc} 2/3&-1/2&1/3\\ -8/3&2&-1/3\\ 1&-1/2&0\end{array}$.