7. Systems of Equations & Matrices

Perform the indicated matrix operations given that A, B and C are defined as follows. If an operation is not defined, state the reason.

A - C

In Exercises 1 - 24, use Gaussian Elimination to find the complete solution to each system of equations, or show that none exists. $\begin{cases}5x + 8y - 6z = 14 \\3x + 4y - 2z = 8 \\x + 2y - 2z = 3\end{cases}$

Solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.

$\begin{cases}3w - 4x + y + z = 9 \\w + x - y - z = 0 \\2w + x + 4y - 2z = 3 \\-w + 2x + y - 3z = 3\end{cases}$

Solve each problem. See Examples 5 and 9. A cashier has a total of 30 bills, made up of ones, fives, and twenties. The number of twenties is 9 more than the number of ones. The total value of the money is \$351. How many of each denomination of bill are there?