Question

Consider the following two systems

-6x-y=2
2x-9y=3
Find the inverse of the (common) coefficient matrix of the two systems.

Answer 1

To find the inverse of the common coefficient matrix of the two systems, you need to find the determinant and then interchange and change the sign of the elements, divided by the determinant.

Step-by-step explanation:

To find the inverse of a matrix, you need to follow these steps:

1. Write down the given matrix.
2. Find the determinant of the matrix.
3. Interchange the diagonal elements of the matrix.
4. Change the sign of the off-diagonal elements of the matrix.
5. Divide the result by the determinant.

In this case, the given matrix is:

6 -1
2 -9

First, find the determinant of the matrix:

Determinant = (6)(-9) - (-1)(2) = -54 - (-2) = -52

Next, interchange the diagonal elements:

Inverse Matrix = -9 -1
2 6

Then, change the sign of the off-diagonal elements:

Inverse Matrix = -9 1
-2 6

Finally, divide the result by the determinant:

Inverse Matrix = (-9/-52) (1/-52)
(-2/-52) (6/-52)

Simplifying the fractions, we get:

Inverse Matrix = 9/52 -1/52
2/52 -3/26