Question

Find the determinant of the matrix. Determine whether the matrix has an inverse, but don't calculate the inverse. [ 2 1 0 ] [ 0-2 4 ] [ 0 1-3 ]

Answer 1

To find the determinant of a 3x3 matrix, use the formula. Calculate the determinant for the given matrix and conclude if it has an inverse.

Step-by-step explanation:

To find the determinant of a 3x3 matrix, you can use the formula:

determinant = a(ei - fh) - b(di - fg) + c(dh - eg)

Let's calculate the determinant for the given matrix:

determinant = 2((-2)(-3) - 4(1)) - 1((0)(-3) - 4(0)) + 0((0)(1) - (-2)(0))

Simplifying the expression, we get:

determinant = 2(-6 + 4) - 1(0 - 0) + 0(0 - 0) = -4

The determinant of the matrix is -4. Since the determinant is non-zero, the matrix has an inverse.