Question

question 26 points 2

solve the given system of equations using the matrix inverse method.
\\(x - y + z = 4\\)
\\(x - 2y - 2z = 9\\)
\\(2x + y + 3z = 1\\)

\\(x = 2, y = 1, z = 1\\)
\\(x = 3, y = -2, z = -1\\)

Explanation:

Set up the matrix equation

Using the Coefficient Matrix knowledge point

$$ A =
LATEXBLOCK0
, \quad X =
LATEXBLOCK1
, \quad B =
LATEXBLOCK2
$$

Find the determinant of the coefficient matrix

Using the Matrix Determinant knowledge point

$$
LATEXBLOCK3
$$

Find the inverse matrix

Using the Matrix Inverse Formula knowledge point

$$ A^{-1} = \frac{1}{8}
LATEXBLOCK4
$$

Solve for the variables

Using the Solving Matrix Equations knowledge point

$$
LATEXBLOCK5
$$

Answer:

• \(x = 2, y = 1, z = 1\)
• \(x = 3, y = -2, z = -1\) (Correct answer)