7. Systems of Equations & Matrices

Write the equations in standard form, then represent the system using an augmented matrix.

$3x+5y-9=0$

$8x=-4y+3$

Perform the indicated Row Operation.

SWAP $R_1\(\leftrightarrow\) R_2$

Perform the indicated Row Operation.

ADD $R_1+2\(\cdot\) R_3\(\rightarrow\) R_1$

Solve the system of equations by using row operations to write a matrix in REDUCED row-echelon form.

$4x+2y+3z=6$

$x+y+z=3$

$5x+y+2z=5$

Write the augmented matrix for each system of linear equations.

$\(\begin{cases}\)2x + y + 2z = 2 \\3x - 5y - z = 4 \(\x\) - 2y - 3z = -6\(\end{cases}\)$

Perform each matrix row operation and write the new matrix.

$\(\begin{bmatrix}\)1 & 2 & 2 & \(\vert\) & 2 \\0 & 1 & -1 & \(\vert\) & 2 \\0 & 5 & 4 & \(\vert\) & 1\(\end{bmatrix}\)-5R_2 + R_3$

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\(\end{bmatrix}\)$