Find the Determinant [[3,2h-1],[h^2,-49]]

Problem

det(3)

Solution

1. Identify the formula for the determinant of a 2×2 matrix [[a,b],[c,d]] which is a*d−b*c

2. Assign the values from the given matrix: a=3 b=2*h−1 c=h2 and d=−49

3. Substitute these values into the determinant formula.

3*(−49)−(2*h−1)*(h2)

4. Multiply the terms to expand the expression.

−147−(2*h3−h2)

5. Distribute the negative sign and simplify the final expression.

−147−2*h3+h2

Final Answer

det(3)=−2*h3+h2−147

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