Question

If A = [-4 5; -7 -2], then det(A) is ______.

Answer 1

43

Explanation:

Here's the matrix you described:

`\left[\begin{array}{ccc}-4&5\\-7&-2\end{array}\right]`

To find the determinant of a 2x2 matrix, simply multiply the diagonally opposite values and subtract them. For example, if the matrix were:

`\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]`

The determinant would be ad - bc.

Applying this same rule to the matrix you used, a = -4, b = 5, c = -7, and d = -2, so:

det(A) = (-4 *-2) - (-7 * 5)

det(A) = 8 - (-35)

det(A) = 8 + 35 = 43