Question

find the inverse of the coefficient matrix \\(\

$$\begin{cases} -3x + 2y = 10 \\\\ 4x - 3y = 7 \\end{cases}$$

\\)

\\(\bigcirc \

$$\begin{bmatrix} -3 & -2 \\\\ -4 & -3 \\end{bmatrix}$$

\\)

\\(\bigcirc \

$$\begin{bmatrix} -3 & 2 \\\\ 4 & -3 \\end{bmatrix}$$

\\)

Explanation:

Identify the coefficient matrix

Using the Coefficient Matrix knowledge point

$$ A =
LATEXBLOCK0
$$

Calculate the determinant

Using the Matrix Determinant knowledge point

$$ \det(A) = (-3)(-3) - (2)(4) = 9 - 8 = 1 $$

Apply the inverse formula

Using the Matrix Inverse Formula knowledge point

$$ A^{-1} = \frac{1}{\det(A)}
LATEXBLOCK1
= \frac{1}{1}
LATEXBLOCK2
=
LATEXBLOCK3
$$

Answer:

• **(A) \(

$$\begin{bmatrix} -3 & -2 \\ -4 & -3 \end{bmatrix}$$

\) (Correct answer)**

• (B) \(

$$\begin{bmatrix} -3 & 2 \\ 4 & -3 \end{bmatrix}$$

\)