Find the Determinant [[0,0,-16],[4,4,16],[0,0,4]]

Problem

det(0)

Solution

1. Identify the matrix and choose a row or column for expansion. Expanding along the first column or the third row is efficient because they contain multiple zeros.

2. Apply the cofactor expansion along the first column. The determinant is the sum of the elements in the column multiplied by their corresponding cofactors.

3. Calculate the terms. The only non-zero term in the first column is at position (2,1) which is the value 4

|A|=(a_11)*(C_11)+(a_21)*(C_21)+(a_31)*(C_31)

|A|=0⋅(C_11)+4⋅(−1)(2+1)*det(0)+0⋅(C_31)

4. Evaluate the 2×2 determinant.

det(0)=(0)*(4)−(−16)*(0)

det(0)=0

5. Multiply the results to find the final determinant value.

|A|=4⋅(−1)⋅0

|A|=0

Final Answer

det(0)=0

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