What is the augmented matrix of the following system?
-3x + 5y = 2
6x + 2y = 7

How many rows and how many columns does this matrix have? What is its dimension?

a. Give the order of each matrix.

b. If $A=\left[a_{ij}\right]$, identify $a_{32}$ and $a_{23}$, or explain why identification is not possible.

$\(\begin{bmatrix}\)4 & -7 & 5 \\-6 & 8 & -1\(\end{bmatrix}\)$

Write the augmented matrix for each system of linear equations.

$\(\begin{cases}\)x - y + z = 8 \\(\y\) - 12z = -15 \\(\z\) = 1\(\end{cases}\)$

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

$\{\begin{array}{c}x+2y+3z=-5\\ 2x+y+z=1\\ x+y-z=8\end{array}$

In Exercises 3–5, solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.

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

$\{\begin{array}{c}3x_1+5x_2-8x_3+5x_4=-8\\ x_1+2x_2-3x_3+x_4=-7\\ 2x_1+3x_2-7x_3+3x_4=-11\\ 4x_1+8x_2-10x_3+7x_4=-10\end{array}$

Write the augmented matrix for each system of linear equations.

$\(\begin{cases}\)5x - 2y - 3z = 0 \\(\x\) + y = 5 \\2x - 3z = 4\(\end{cases}\)$

Use the given row transformation to change each matrix as indicated.