Find the inverse of the matrix

Question

[1 2 3 1]

Answer 1

The given matrix is [1 2 3 1].

To find the inverse of the matrix, we need to use the formula for a 2x2 matrix:

[A B]
[C D]

The inverse matrix is given by:

1/(AD - BC) * [D -B]
[-C A]

In this case, A=1, B=2, C=3, and D=1.

So the inverse matrix is:

1/(1(1) - 2(3)) * [1 -2]
[-3 1]

Simplifying further:

1/(-5) * [1 -2]
[-3 1]

The inverse of the given matrix is:

[-1/5 2/5]
[ 3/5 -1/5]