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:

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<reasoning>

Calculate the determinant of the matrix

Using the Matrix Determinant knowledge point
\[
\det(A) = \det

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

= (-4)(-2) - (-2)(-4) = 8 - 8 = 0
\]

Determine if the inverse exists

Using the Matrix Inverse Existence and Singular Matrix knowledge points
\[
\det(A) = 0 \implies A \text{ is singular} \implies A^{-1} \text{ does not exist}
\]
</reasoning>

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

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

\)</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) = \det

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

= (-4)(-2) - (-2)(-4) = 8 - 8 = 0
\]

Determine if the inverse exists

Using the Matrix Inverse Existence and Singular Matrix knowledge points
\[
\det(A) = 0 \implies A \text{ is singular} \implies A^{-1} \text{ does not exist}
\]
</reasoning>

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

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

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

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