Find the Inverse [[1,-7],[-8,0]]

Problem

[[1,−7],[−8,0]]

Solution

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

A=[[a,b],[c,d]]=[[1,−7],[−8,0]]

A(−1)=1/(a*d−b*c)*[[d,−b],[−c,a]]

2. Calculate the determinant of the matrix using the formula det(A)=a*d−b*c

det(A)=(1)*(0)−(−7)*(−8)

det(A)=0−56

det(A)=−56

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

[[d,−b],[−c,a]]=[[0,7],[8,1]]

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

A(−1)=1/(−56)*[[0,7],[8,1]]

5. Simplify the matrix by distributing the scalar across all elements.

A(−1)=[[0,−7/56],[−8/56,−1/56]]

A(−1)=[[0,−1/8],[−1/7,−1/56]]

Final Answer

[[1,−7],[−8,0]](−1)=[[0,−1/8],[−1/7,−1/56]]

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