##### Practice Midterm SOLUTION: #1
abbyto1607
For problem 1, we are given a set of equations, and asked to solve using Gauss-Jordan elimination. $\begin{array}{ccc} 2x+3y+4z+w=1 \\ x-3y+z=2\\ x+2z-w=8 \end{array}$ In matrix form, this is $\begin{array}{ccc} 2&3&4&1&1 \\ 1&-3&1&0&2 \\ 1&0&2&-1&8 \end{array}$
abbyto1607: May 5, 2015, 4:38 p.m.
Sorry, finger slipped before I finished writing the solution.
abbyto1607: May 5, 2015, 4:38 p.m.
Sorry, finger slipped before I finished writing the solution.
abbyto1607: May 5, 2015, 4:42 p.m.
Using Gauss-Jordan elimination, I arrived at the matrix $\begin{array}{ccc} 1&0&0&7&|-34 \\ 0&1&0&1&|-5\\ 0&0&1&-4&|21 \end{array}$ This is the row reduced form of the original matrix. This RREF matrix gives that $\begin{array}{ccc} x \\ y \\ z \\ w\end{array}$ = $\begin{array}{ccc} -34-7w \\ -5-w \\ 21+4w\\ w& i \end{array}$ where $w$ is an arbitrary value.
abbyto1607: May 5, 2015, 4:43 p.m.
Please ignore the "i". That was a typo.
abbyto1607: May 5, 2015, 5:22 p.m.
abbyto1607 = Abigail To (dis 1B)