Find the Inverse A=[[2,1],[4,2]]

Problem

A=[[2,1],[4,2]]

Solution

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

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

3. Substitute the values a=2 b=1 c=4 and d=2 into the determinant formula.

det(A)=(2)*(2)−(1)*(4)

4. Simplify the result of the determinant calculation.

det(A)=4−4

det(A)=0

5. Conclude that because the determinant is zero, the matrix is singular and does not have an inverse.

Final Answer

A(−1)=Does not exist (Matrix is singular)

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