Questions: What linear system of equations does the matrix represent? 19. [9 -11 -2; -14 11 8] a. 9x = -14; -11x = 11; -2x = 8 c. 9x - 11y = -2; -14x + 11y = 8 b. 9x - 11y = 2; -14x + 11y = -8 d. 9x = -14; -11x = 11; 2x = -8

What linear system of equations does the matrix represent?
19. [9 -11 -2; -14 11 8]
a. 9x = -14; -11x = 11; -2x = 8
c. 9x - 11y = -2; -14x + 11y = 8
b. 9x - 11y = 2; -14x + 11y = -8
d. 9x = -14; -11x = 11; 2x = -8

Transcript text: What linear system of equations does the matrix represent? 19. $\left[\begin{array}{cc|c}9 & -11 & -2 \\ -14 & 11 & 8\end{array}\right]$ a. $\left\{\begin{array}{l}9 x=-14 \\ -11 x=11 \\ -2 x=8\end{array}\right.$ c. $\left\{\begin{array}{l}9 x-11 y=-2 \\ -14 x+11 y=8\end{array}\right.$ b. $\left\{\begin{array}{l}9 x-11 y=2 \\ -14 x+11 y=-8\end{array}\right.$ d. $\left\{\begin{array}{l}9 x=-14 \\ -11 x=11 \\ 2 x=-8\end{array}\right.$

Solution

Solution Steps

Step 1: Identify the matrix representation

The given matrix is: \[ \left[\begin{array}{cc|c} 9 & -11 & -2 \\ -14 & 11 & 8 \end{array}\right] \] This is an augmented matrix representing a system of linear equations.

Step 2: Convert the matrix to a system of equations

The augmented matrix corresponds to the following system of equations: \[ \begin{cases} 9x - 11y = -2 \\ -14x + 11y = 8 \end{cases} \]

Step 3: Compare with the given options

Compare the derived system of equations with the provided options: