Question

Find the inverse of the matrix if it exists. [ 2 4 1 ] [ -1 1-1] [ 1 4 0 ]

Answer 1

To find the inverse of a matrix, calculate the determinant and verify its value.

Step-by-step explanation:

To find the inverse of a matrix, we use the formula:

A-1 = (1/det(A)) * adj(A)

where A is the given matrix, det(A) is the determinant of A, and adj(A) is the adjugate of A.

Let's calculate the inverse step by step:

1. Calculate the determinant of A: det(A) = (2 imes 1 imes 0) + (4 imes -1 imes 1) + (1 imes 1 imes 4) = 0 - 4 + 4 = 0
2. Since the determinant is 0, the inverse does not exist.