Find the Inverse [[-4,10],[5,6]]

Problem

[[−4,10],[5,6]](−1)

Solution

1. Identify the matrix A and its elements.

A=[[a,b],[c,d]]=[[−4,10],[5,6]]

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

det(A)=(−4)*(6)−(10)*(5)

det(A)=−24−50

det(A)=−74

3. Apply the inverse formula for a 2×2 matrix, which is A(−1)=1/det(A)*[[d,−b],[−c,a]]

A(−1)=1/(−74)*[[6,−10],[−5,−4]]

4. Distribute the scalar to each element of the matrix.

A(−1)=[[6/(−74),(−10)/(−74)],[(−5)/(−74),(−4)/(−74)]]

5. Simplify the fractions by dividing by common factors.

A(−1)=[[−3/37,5/37],[5/74,2/37]]

Final Answer

[[−4,10],[5,6]](−1)=[[−3/37,5/37],[5/74,2/37]]

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