Find the Determinant [[5,4],[2,1]]

Problem

det(5)

Solution

1. Identify the components of the 2×2 matrix [[a,b],[c,d]] where a=5 b=4 c=2 and d=1

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

3. Substitute the values into the formula to get 5⋅1−4⋅2

4. Simplify the expression by performing the multiplication and subtraction: 5 - 8 = -3$.

Final Answer

det(5)=−3

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