Find the Determinant of the Resulting Matrix 3[[1,3],[4,2]]-[[3,3],[4,4]]

Problem

det(3*[[1,3],[4,2]]−[[3,3],[4,4]])

Solution

1. Perform scalar multiplication by multiplying every entry in the first matrix by 3.

3*[[1,3],[4,2]]=[[3,9],[12,6]]

2. Subtract the matrices by subtracting corresponding entries.

[[3,9],[12,6]]−[[3,3],[4,4]]=[[0,6],[8,2]]

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

det(0)=(0)*(2)−(6)*(8)

4. Simplify the arithmetic to find the final value.

0−48=−48

Final Answer

det(3*[[1,3],[4,2]]−[[3,3],[4,4]])=−48

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