Question

Let a be the coefficient matrix of the system. Find a-1.

Answer 1

To find the inverse of a coefficient matrix, you can use the method of finding the adjugate matrix and dividing it by the determinant of the original matrix.

Step-by-step explanation:

The Inverse of a matrix is denoted by A-1. To find the inverse of a coefficient matrix, you can use the method of finding the adjugate matrix and dividing it by the determinant of the original matrix.

Here are the steps:

1. Calculate the determinant of the coefficient matrix.
2. Find the adjugate matrix by finding the cofactor of each element of the matrix and then transposing it.
3. Finally, divide each element of the adjugate matrix by the determinant.

For example, let's say the coefficient matrix is [a b; c d]. The inverse matrix A-1 would be [(1/det) * d, (-1/det) * b; (-1/det) * c, (1/det) * a].