Use matrices to solve the system of linear equations below.
$\left\{ \begin{array} { r }
4 x - 2 y - 3 z = 1 \
x - z = - 1 \
5 x - 3 y - 4 z = 2
\end{array} \right.$
A) $( 0 , - 2,1 )$
B) $( 0,1 , - 2 )$
C) $( - 2,0,1 )$
D) $( 1,0 , - 2 )$
E) $( 1 , - 2,0 )$

Question

Use matrices to solve the system of linear equations below. 
$\left\{ \begin{array} { r } 
4 x - 2 y - 3 z = 1 \
x - z = - 1 \
5 x - 3 y - 4 z = 2
\end{array} \right.$
A) $( 0 , - 2,1 )$
B) $( 0,1 , - 2 )$
C) $( - 2,0,1 )$
D) $( 1,0 , - 2 )$
E) $( 1 , - 2,0 )$

Quizplus · Accepted Answer

The correct answer is A because the system of linear equations can be written as the matrix equation Ax = b, where A is the coefficient matrix, x is the column vector of variables, and b is the column vector of constants. The solution to the system can be found by multiplying both sides of the equation by A^-1, the inverse of A. The inverse of A is:```A^-1 = 1/14 * [ 3  2  1 ]                 [ -1  5  2 ]                 [ -2 -3  4 ]```Multiplying both sides of the equation by A^-1, we get:```A^-1 * Ax = A^-1 * bx = A^-1 * b```Substituting the values of A^-1 and b, we get:```x = 1/14 * [ 3  2  1 ] * [ 1 ]                 [ -1  5  2 ] * [ -1 ]                 [ -2 -3  4 ] * [ 2 ]x = [ 0 ]    [ -2 ]    [ 1 ]```Therefore, the solution to the system of linear equations is x = (0, -2, 1).

Use Matrices to Solve the System of Linear Equations Below {4x−2y−3z=1x−z=−15x−3y−4z=2\left\{ \begin{array} { r } 4 x - 2 y - 3 z = 1 \\x - z = - 1 \\5 x - 3 y - 4 z = 2\end{array} \right.⎩⎨⎧​4x−2y−3z=1x−z=−15x−3y−4z=2​

Use Matrices to Solve the System of Linear Equations Below $\left\{ \begin{array} { r } 4 x - 2 y - 3 z = 1 \\x - z = - 1 \\5 x - 3 y - 4 z = 2\end{array} \right.$