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:

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

$$ \det(A) = -22 eq 0 \implies \text{The matrix is invertible.} $$

Answer:

• **Yes, determinant of the matrix \(

eq 0\) (Correct answer)**

• No, determinant of the matrix \(= 0\)