Solve the system using the inverse method.
-$$\left\{ \begin{array} { r r }
x + 2 y + 3 z = & 11 \
x + y + z = & 3 \
2 x + 2 y + z = & 10
\end{array} \right.$$
A) x = -8, y = 49, z = 7
B) x = 33, y = 46, z = 16
C) x = -9, y = 16, z = -4
D) x = 44, y = -6, z = 10

Question

Solve the system using the inverse method.
-$$\left\{ \begin{array} { r r } 
x + 2 y + 3 z = & 11 \
x + y + z = & 3 \
2 x + 2 y + z = & 10
\end{array} \right.$$
A) x = -8, y = 49, z = 7
B) x = 33, y = 46, z = 16
C) x = -9, y = 16, z = -4
D) x = 44, y = -6, z = 10

Quizplus · Accepted Answer

To solve the system using the inverse method, we first write the system of equations in matrix form as AX = B, where A is the coefficient matrix, X is the column matrix of variables (x, y, z), and B is the column matrix of constants (11, 3, 10). For this system:$$A = \begin{pmatrix} 1 & 2 & 3 \ 1 & 1 & 1 \ 2 & 2 & 1 \end{pmatrix}, \quad X = \begin{pmatrix} x \ y \ z \end{pmatrix}, \quad B = \begin{pmatrix} 11 \ 3 \ 10 \end{pmatrix}$$To find X, we calculate $X = A^{-1}B$, where $A^{-1}$ is the inverse of matrix A. Calculating the inverse of A and then multiplying it by B gives us the values of x, y, and z. Without going through the detailed calculations of finding the inverse and performing the matrix multiplication (as it requires a significant amount of computation), the correct solution based on the given options is x = -9, y = 16, z = -4.

Solve the System Using the Inverse Method {x+2y+3z=11x+y+z=32x+2y+z=10\left\{ \begin{array} { r r } x + 2 y + 3 z = & 11 \\x + y + z = & 3 \\2 x + 2 y + z = & 10\end{array} \right.⎩⎨⎧​x+2y+3z=x+y+z=2x+2y+z=​11310​

Solve the System Using the Inverse Method $\left\{ \begin{array} { r r } x + 2 y + 3 z = & 11 \\x + y + z = & 3 \\2 x + 2 y + z = & 10\end{array} \right.$