Question

which system of equations can be solved using this matrix equation?
\\(\

$$\begin{bmatrix} 5 & 2 & 1 \\\\ 7 & -5 & 2 \\\\ -5 & 3 & 1 \\end{bmatrix}$$

\

$$\begin{bmatrix} x \\\\ y \\\\ z \\end{bmatrix}$$

= \

$$\begin{bmatrix} 16 \\\\ 3 \\\\ 12 \\end{bmatrix}$$

\\)

\\(\circ\\) a. \\(\

$$\begin{align} 5x + 7y - 5z &= 16 \\\\ 2x - 5y + 3z &= 3 \\\\ x + 2y + z &= 12 \\end{align}$$

\\)

\\(\circ\\) b. \\(\

$$\begin{align} 5x + 2y + z &= 16 \\\\ 7x - 5y + 2z &= 3 \\\\ -5x + 3y + z &= 12 \\end{align}$$

\\)

\\(\circ\\) c. \\(\

$$\begin{align} 5x + 2x + x &= 16 \\\\ 7y - 5y + 2y &= 3 \\\\ -5z + 3z + z &= 12 \\end{align}$$

\\)

\\(\circ\\) d. \\(\

$$\begin{align} 5x + 7y - 5z &= 12 \\\\ 2x - 5y + 3z &= 3 \\\\ x + 2y + z &= 16 \\end{align}$$

\\)

Explanation:

Step1: Multiply first row & vector

$5x + 2y + 1z = 16$

Step2: Multiply second row & vector

$7x -5y + 2z = 3$

Step3: Multiply third row & vector

$-5x + 3y + 1z = 12$

Answer:

B. $5x + 2y + z = 16$
$7x - 5y + 2z = 3$
$-5x + 3y + z = 12$