Question

find the inverse of the given matrix \\(\

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

\\).

\\(\bigcirc\\) the inverse does not exist

\\(\bigcirc\\) \\(\

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

\\)

Explanation:

Calculate the determinant of the matrix

Using the Matrix Determinant knowledge point

$$ \det(A) = \det
LATEXBLOCK0
= (-4)(-2) - (-2)(-4) = 8 - 8 = 0 $$

Determine if the inverse exists

Using the Matrix Inverse Existence and Singular Matrix knowledge points

$$ \det(A) = 0 \implies A \text{ is singular} \implies A^{-1} \text{ does not exist} $$

Answer:

• The inverse does not exist (Correct answer)
• \(

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

\)