Find the Determinant [[7,5,0],[4,5,8],[0,-1,5]]

Problem

det(7)

Solution

1. Identify the matrix and choose a row or column for expansion. We will expand along the first row.

2. Apply the formula for the determinant of a 3×3 matrix using the elements of the first row: (a_11) (a_12) and (a_13)

det(A)=7*det(5)−5*det(4)+0*det(4)

3. Calculate the 2×2 determinants using the formula a*d−b*c

det(5)=(5)*(5)−(8)*(−1)=25+8=33

det(4)=(4)*(5)−(8)*(0)=20−0=20

4. Substitute the values back into the expansion equation.

det(A)=7*(33)−5*(20)+0

5. Simplify the expression to find the final value.

det(A)=231−100=131

Final Answer

det(7)=131

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