Answer:
Explanation:
To find the inverse of a matrix, we need to put it in the reduced row echelon form (RREF) using elementary row operations. We can augment the given matrix with an identity matrix of the same size, and then apply the row operations to both matrices simultaneously until the left-hand side becomes an identity matrix. The right-hand side will then be the inverse of the original matrix.
Here are the steps:
[ 5 3 | 1 0 ]
[13 8 | 0 1 ]
R1/5 -> R1:
[ 1 3/5 | 1/5 0 ]
[13 8 | 0 1 ]
R2-13R1 -> R2:
[ 1 3/5 | 1/5 0 ]
[ 0 1/5 | -13 1 ]
R1-(3/5)R2 -> R1:
[ 1 0 | 26/5 -3/5 ]
[ 0 1 | -13 1/5 ]
So, the inverse matrix is:
[ 26/5 -3/5 ]
[-13 1/5 ]