Find the Determinant of the Resulting Matrix [[7,2],[1,3]]-[[1,2],[5,6]]

Problem

det([[7,2],[1,3]]−[[1,2],[5,6]])

Solution

1. Subtract the two matrices by subtracting corresponding entries.

[[7,2],[1,3]]−[[1,2],[5,6]]=[[7−1,2−2],[1−5,3−6]]

2. Simplify the resulting matrix.

[[6,0],[−4,−3]]

3. Apply the formula for the determinant of a 2×2 matrix, which is det(a)=a*d−b*c

det(6)=(6)*(−3)−(0)*(−4)

4. Calculate the final numerical value.

−18−0=−18

Final Answer

det([[7,2],[1,3]]−[[1,2],[5,6]])=−18

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