Find the Determinant [[3,0,4],[2,3,2],[0,5,-1]]

Problem

det(3)

Solution

1. Identify the matrix and choose a row or column for expansion. Expanding along the first row is convenient because it contains a zero.

2. Apply the cofactor expansion formula along the first row. The determinant is calculated as the sum of the elements multiplied by their corresponding minors and signs.

|A|=3⋅det(3)−0⋅det(2)+4⋅det(2)

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

det(3)=(3)*(−1)−(2)*(5)=−3−10=−13

det(2)=(2)*(5)−(3)*(0)=10−0=10

4. Substitute the values back into the expansion equation.

|A|=3*(−13)−0+4*(10)

5. Simplify the expression to find the final value.

|A|=−39+40=1

Final Answer

det(3)=1

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