Final answer:
To find the determinant of the matrix and determine 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)
For the given matrix [0 1 0], [2 6 4], [1 0 3], the elements are:
- a = 0
- b = 1
- c = 0
- d = 2
- e = 6
- f = 4
- g = 1
- h = 0
- i = 3
Plugging these values into the formula, we get:
determinant = 0(6 * 3 - 0 * 0) - 1(2 * 3 - 4 * 0) + 0(2 * 0 - 6 * 1) = 0 - 6 + 0 = -6
Since the determinant is not equal to 0, the given matrix has an inverse.