Question

question 23 points 2

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

\\(x = 1/5, y = 3/5, z = 8/7\\)
\\(x = -8/7, y = 10/7, z = 19/7\\)

Explanation:

Write the system in matrix form

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 inverse matrix of A

Using the Matrix Inverse Formula knowledge point

$$ C =
LATEXBLOCK4
\implies A^{-1} = \frac{1}{14}
LATEXBLOCK5
$$

Solve for the variable vector X

Using the Solving Matrix Equations knowledge point

$$
LATEXBLOCK6
$$

Answer:

• (A) \(x = 1/5, y = 3/5, z = 8/7\)
• (B) \(x= -8/7, y = 10/7, z = 19/7\) (Correct answer)