Question

Is x=[-28-12] the inverse of a=[12-214-12]?

1) Yes, x and a are inverses of each other.
2) No, x and a are not inverses of each other.
3) Cannot be determined.

Answer 1

Since matrix a is not a square matrix and does not conform to the dimensions of matrix x for multiplication, it cannot be determined whether x is the inverse of a.

To determine if x is the inverse of matrix a, the product of matrix a and matrix x should result in the identity matrix. Given matrix a as a = [12 -2 14 -1 2] and matrix x as x = [-2 8 -1 2], we can compute the multiplication of a*x.

First, let's multiply the matrices:

[12 -2] [-2 8]
[14 -1 2] * [-1 2]

Since matrix a is not a square matrix, and also because the dimensions of a do not conform to the dimensions of x for multiplication (2x3 multiplied by 2x2 is not defined), we cannot perform the multiplication. Therefore, we cannot conclude if x is the inverse of a.

The correct answer is: 3) Cannot be determined.