Find the Inverse [[1,-3],[2,4]]

Problem

[[1,−3],[2,4]]

Solution

1. Identify the matrix A and its elements a=1 b=−3 c=2 and d=4

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

det(A)=(1)*(4)−(−3)*(2)

det(A)=4−(−6)

det(A)=10

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

A(−1)=1/10*[[4,3],[−2,1]]

4. Distribute the scalar 1/10 to each element in the matrix.

A(−1)=[[4/10,3/10],[(−2)/10,1/10]]

5. Simplify the fractions within the matrix.

A(−1)=[[2/5,3/10],[−1/5,1/10]]

Final Answer

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

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