Solve the system using the inverse method.
-$$\left\{ \begin{array} { l }
x + 2 y + 3 z = 10 \
x + y + z = 2 \
x - 2 z = - 1
\end{array} \right.$$
A) x = -11, y = 18, z = -5
B) x = 27, y = 38, z = 13
C) x = 10, y = 0, z = 0
D) x = -13, y = 28, z = -5

Question

Solve the system using the inverse method.
-$$\left\{ \begin{array} { l } 
x + 2 y + 3 z = 10 \
x + y + z = 2 \
x - 2 z = - 1
\end{array} \right.$$
A) x = -11, y = 18, z = -5
B) x = 27, y = 38, z = 13
C) x = 10, y = 0, z = 0
D) x = -13, y = 28, z = -5

Quizplus · Accepted Answer

To solve the system using the inverse method, first, we write the system of equations in matrix form AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix. For the given system, we have:$$A = \begin{pmatrix} 1 & 2 & 3 \ 1 & 1 & 1 \ 1 & 0 & -2 \end{pmatrix}, \quad X = \begin{pmatrix} x \ y \ z \end{pmatrix}, \quad B = \begin{pmatrix} 10 \ 2 \ -1 \end{pmatrix}$$To find X, we calculate $X = A^{-1}B$. Without performing the detailed calculations here (which involve finding the inverse of A and then multiplying it by B), the correct solution to the system is given by option A: $x = -11$, $y = 18$, $z = -5$. This is determined by performing the matrix calculations or using a computational tool capable of handling matrix operations.

Solve the System Using the Inverse Method {x+2y+3z=10x+y+z=2x−2z=−1\left\{ \begin{array} { l } x + 2 y + 3 z = 10 \\x + y + z = 2 \\x - 2 z = - 1\end{array} \right.⎩⎨⎧​x+2y+3z=10x+y+z=2x−2z=−1​

Solve the System Using the Inverse Method $\left\{ \begin{array} { l } x + 2 y + 3 z = 10 \\x + y + z = 2 \\x - 2 z = - 1\end{array} \right.$