Question

question 24 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:

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<reasoning>

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
\[
\det(A) = 0 \implies A^{-1} \text{ does not exist}
\]
</reasoning>

<answer>
<mcq-correct>The inverse does not exist.</mcq-correct>
<mcq-option>\(

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

\)</mcq-option>
</answer>

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Answer:

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<reasoning>

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
\[
\det(A) = 0 \implies A^{-1} \text{ does not exist}
\]
</reasoning>

<answer>
<mcq-correct>The inverse does not exist.</mcq-correct>
<mcq-option>\(

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

\)</mcq-option>
</answer>

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