Question

question 31 points 2

is the matrix \\(\

$$\begin{bmatrix} 4 & -6 \\\\ -5 & 2 \\end{bmatrix}$$

\\) invertible? why or why not?

yes, determinant of the matrix \\(\
eq 0\\)
no, determinant of the matrix \\(= 0\\)

Explanation:

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<reasoning>

Calculate the determinant of the matrix

Using the Matrix Determinant knowledge point
\[
\det(A) = (4)(2) - (-6)(-5) = 8 - 30 = -22
\]

Determine invertibility based on the determinant

Using the Matrix Inverse Existence knowledge point
\[
\det(A) = -22
eq 0 \implies \text{The matrix is invertible.}
\]
</reasoning>

<answer>
<mcq-correct>Yes, determinant of the matrix \(
eq 0\)</mcq-correct>
<mcq-option>No, determinant of the matrix \(= 0\)</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
\[
\det(A) = (4)(2) - (-6)(-5) = 8 - 30 = -22
\]

Determine invertibility based on the determinant

Using the Matrix Inverse Existence knowledge point
\[
\det(A) = -22
eq 0 \implies \text{The matrix is invertible.}
\]
</reasoning>

<answer>
<mcq-correct>Yes, determinant of the matrix \(
eq 0\)</mcq-correct>
<mcq-option>No, determinant of the matrix \(= 0\)</mcq-option>
</answer>

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