Question

question 34 points 2

solve the system of equations using the matrix inverse method.
\\(x + 2y - 3z = -4\\)
\\(2x + 3y + 2z = 2\\)
\\(3x - 3y - 4z = 11\\).

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

Explanation:

Set up the matrix equation

Using the Coefficient Matrix knowledge point

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

Calculate the determinant of A

Using the Matrix Determinant knowledge point

$$
LATEXBLOCK3
$$

Find the adjugate matrix of A

Using the Adjoint Matrix and Cofactor Matrix knowledge points

$$
LATEXBLOCK4
$$

Compute the inverse matrix of A

Using the Matrix Inverse Formula knowledge point

$$ A^{-1} = \frac{1}{67}
LATEXBLOCK5
$$

Solve for the variable vector X

Using the Solving Matrix Equations knowledge point

$$
LATEXBLOCK6
$$

Answer:

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