Find the Inverse [[6,5],[2,2]]

Problem

[[6,5],[2,2]]

Solution

1. Identify the matrix A and the formula for the inverse of a 2×2 matrix.

A=[[a,b],[c,d]]=[[6,5],[2,2]]

A(−1)=1/det(A)*[[d,−b],[−c,a]]

2. Calculate the determinant of the matrix.

det(A)=(6)*(2)−(5)*(2)

det(A)=12−10

det(A)=2

3. Swap the elements on the main diagonal and change the signs of the elements on the off-diagonal.

[[d,−b],[−c,a]]=[[2,−5],[−2,6]]

4. Multiply the resulting matrix by the reciprocal of the determinant.

A(−1)=1/2*[[2,−5],[−2,6]]

A(−1)=[[2/2,(−5)/2],[(−2)/2,6/2]]

5. Simplify the fractions to find the final inverse matrix.

A(−1)=[[1,−2.5],[−1,3]]

Final Answer

[[6,5],[2,2]](−1)=[[1,−2.5],[−1,3]]

Want more problems? Check here!