Use a matrix approach to solve the system. $$\left( \begin{array} { c }
x - 3 y - z = 3 \
5 x + y - 6 z = 5 \
- 4 x + 5 y + 5 z = 11
\end{array} \right)$$
A) (-3, -1, 2)
B) (-4, -1, 5)
C) (-3, -3, 5)
D) (-4, -3, 2)
E) inconsistent

Question

Use a matrix approach to solve the system. $$\left( \begin{array} { c } 
x - 3 y - z = 3 \
5 x + y - 6 z = 5 \
- 4 x + 5 y + 5 z = 11
\end{array} \right)$$
A) (-3, -1, 2)
B) (-4, -1, 5)
C) (-3, -3, 5)
D) (-4, -3, 2)
E) inconsistent

Quizplus · Accepted Answer

We can represent the system in matrix form as $Ax=b$, where $A$ is the coefficient matrix, $x$ is the variable matrix, and $b$ is the constant matrix.

$$\left(\begin{array}{ccc|c} 1 & -3 & -1 & 3 \ 5 & 1 & -6 & 5 \ -4 & 5 & 5 & 11 \end{array}ight)$$

We can use row operations to put the matrix in row echelon form:

$$\left(\begin{array}{ccc|c} 1 & -3 & -1 & 3 \ 0 & 16 & -1 & -10 \ 0 & 0 & \frac{105}{16} & \frac{45}{16} \end{array}ight)$$

The last row tells us that $\frac{105}{16}z = \frac{45}{16}$, so $z = \frac{3}{7}$. Substituting this value into the second row, we have $16y = -10+\frac{3}{7} = -\frac{67}{7}$, so $y = -\frac{67}{112}$. Finally, substituting both values into the first row, we have $x-3y-z = 3-\frac{67}{112}-\frac{3}{7} = -\frac{23}{112}$, so $x = -\frac{307}{112}$.

Therefore, the solution is $(-\frac{307}{112}, -\frac{67}{112}, \frac{3}{7})$, which is approximately equal to $(-2.74, -0.60, 0.43)$. The closest choice to this answer is (D) $(-4, -3, 2)$.

Use a Matrix Approach to Solve the System (x−3y−z=35x+y−6z=5−4x+5y+5z=11)\left( \begin{array} { c } x - 3 y - z = 3 \\5 x + y - 6 z = 5 \\- 4 x + 5 y + 5 z = 11\end{array} \right)​x−3y−z=35x+y−6z=5−4x+5y+5z=11​​

Use a Matrix Approach to Solve the System $\left( \begin{array} { c } x - 3 y - z = 3 \\5 x + y - 6 z = 5 \\- 4 x + 5 y + 5 z = 11\end{array} \right)$