Find the value of `|[5,3],[-7,-4]|`

Options

A. `-1`
B. `-41`
C. 41
D. 1

Explanation

To find the value of the determinant \(|[5, 3], [-7, -4]|\), we can use the formula for the determinant of a 2x2 matrix. The determinant of a matrix \(\begin{bmatrix} a & b \\ c & d \end{bmatrix}\) is given by:

\[ |A| = ad - bc \]

In our case, the matrix is:

\[ \begin{bmatrix} 5 & 3 \\ -7 & -4 \end{bmatrix} \]

Here, we can identify the elements as follows:
- \(a = 5\)
- \(b = 3\)
- \(c = -7\)
- \(d = -4\)

Now, we can substitute these values into the determinant formula:

\[ |A| = (5 \cdot -4) - (3 \cdot -7) \]

Calculating each term:

1. Calculate \(5 \cdot -4\):
\[ 5 \cdot -4 = -20 \]

2. Calculate \(3 \cdot -7\):
\[ 3 \cdot -7 = -21 \]

Now, substituting these results back into the determinant formula:

\[ |A| = -20 - (-21) \]

This simplifies to:

\[ |A| = -20 + 21 = 1 \]

Thus, the value of the determinant \(|[5, 3], [-7, -4]|\) is:

\[ \boxed{1} \]