Find the Inverse [[5,10],[3,6]]

Problem

[[5,10],[3,6]]

Solution

1. Identify the matrix A and its elements.

A=[[a,b],[c,d]]=[[5,10],[3,6]]

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

det(A)=(5)*(6)−(10)*(3)

3. Simplify the determinant calculation.

det(A)=30−30

det(A)=0

4. Determine invertibility based on the result. A matrix is invertible if and only if its determinant is non-zero.

0=0

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

Final Answer

The inverse of *[[5,10],[3,6]]* does not exist.

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