Question

question 28 points 2

find the inverse of the matrix.
\\\

$$\begin{bmatrix} -9 & -9 \\\\ -2 & -2 \\end{bmatrix}$$

\\

• the inverse does not exist.
• \\\

$$\begin{bmatrix} -9 & 9 \\\\ -2 & -2 \\end{bmatrix}$$

\\

Explanation:

Define the given matrix

Using the Matrix Determinant knowledge point

$$ A =
LATEXBLOCK0
$$

Calculate the determinant of the matrix

Using the Matrix Determinant knowledge point

$$ \det(A) = (-9)(-2) - (-9)(-2) = 18 - 18 = 0 $$

Determine if the inverse exists

Using the Matrix Inverse Existence knowledge point

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

Answer:

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

$$\begin{bmatrix} -9 & 9 \\ -2 & -2 \end{bmatrix}$$

\)