Use matrices to solve the system of equations. $\left\{ \begin{array} { l }
x + y + z = 6 \
x + 3 y + z = 8 \
x + y + 3 z = 12
\end{array} \right.$
A) $( 1,2,3 )$
B) $( - 2 , - 1 , - 3 )$
C) $( 2,1,3 )$
D) no solution
E) infinitely many solutions

Question

Use matrices to solve the system of equations. $\left\{ \begin{array} { l } 
x + y + z = 6 \
x + 3 y + z = 8 \
x + y + 3 z = 12
\end{array} \right.$
A) $( 1,2,3 )$
B) $( - 2 , - 1 , - 3 )$
C) $( 2,1,3 )$
D) no solution
E) infinitely many solutions

Quizplus · Accepted Answer

The system of equations can be represented by the matrix equation $AX = B$, where $A = \begin{bmatrix} 1 & 1 & 1 \ 1 & 3 & 1 \ 1 & 1 & 3 \end{bmatrix}$, $X = \begin{bmatrix} x \ y \ z \end{bmatrix}$, and $B = \begin{bmatrix} 6 \ 8 \ 12 \end{bmatrix}$. Solving this matrix equation using methods such as Gaussian elimination or matrix inversion gives the solution $X = \begin{bmatrix} 2 \ 1 \ 3 \end{bmatrix}$, which corresponds to the choice $(2, 1, 3)$.

Use Matrices to Solve the System of Equations {x+y+z=6x+3y+z=8x+y+3z=12\left\{ \begin{array} { l } x + y + z = 6 \\x + 3 y + z = 8 \\x + y + 3 z = 12\end{array} \right.⎩⎨⎧​x+y+z=6x+3y+z=8x+y+3z=12​

Use Matrices to Solve the System of Equations $\left\{ \begin{array} { l } x + y + z = 6 \\x + 3 y + z = 8 \\x + y + 3 z = 12\end{array} \right.$