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

Problem

[[1,2],[2,4]]

Solution

1. Identify the matrix A and its components a=1 b=2 c=2 and d=4

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

3. Substitute the values into the determinant formula:

det(A)=(1)*(4)−(2)*(2)

4. Simplify the result:

det(A)=4−4=0

5. Determine invertibility based on the determinant. Since the determinant is 0 the matrix is singular.

6. Conclude that a matrix with a determinant of zero does not have an inverse.

Final Answer

[[1,2],[2,4]](−1)=Does not exist (Singular Matrix)

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