Question

Is x = [−28−12] the inverse of a = [14−114−12]?

Answer 1

No, x = [-28 -12] is not the inverse of a = [14 -11 4 -12].

Step-by-step explanation:

No, x = [-28 -12] is not the inverse of a = [14 -11 4 -12]. To find the inverse of a matrix, we need to calculate the determinant of the matrix. If the determinant is non-zero, then the matrix has an inverse. If the determinant is zero, the matrix does not have an inverse.

In this case, the determinant of matrix a is:

det(a) = 14*(-12)-(4*(-11)) = -168-(-44) = -124

Since the determinant is non-zero, matrix a has an inverse. However, to find the actual inverse, we need to multiply the adjugate of matrix a by the inverse of the determinant. So, x = [-28 -12] is not the correct inverse of matrix a.

Answer 2

No, x = [-28 -12] is not the inverse of a = [14 -1 14 -12].

Here's why:

1. Definition of Matrix Inverse:

- The inverse of a matrix A, denoted as A^(-1), is a matrix that, when multiplied by A, yields the identity matrix I.

- The identity matrix I is a square matrix with 1s on the diagonal and 0s elsewhere.

2. Matrix Multiplication:

- To check if two matrices are inverses, we multiply them and see if the result is the identity matrix.

3. Multiplying a and x:

a * x = [14 -1 14 -12] * [-28 -12]

= [(14*-28) + (-1*-12) (14*-12) + (-1*-12)]

= [-380 0]

- The result is not the identity matrix. It's a 2x1 matrix with -380 in the first element and 0 in the second element.

4. Conclusion:

- Since a * x does not equal the identity matrix, x is not the inverse of a.