Find the Determinant

Problem

det(1)

Solution

1. Perform row operations to create zeros in the first column. Add row 1 to row 2 ((R_2)+(R_1)⇒(R_2), subtract row 1 from row 3 ((R_3)−(R_1)⇒(R_3), and subtract row 1 from row 4 ((R_4)−(R_1)⇒(R_4).

det(1)

2. Expand along the first column to reduce the matrix to a 3×3 determinant.

1⋅det(−2)

3. Expand along the first row of the 3×3 matrix, as it contains two zeros.

−2⋅det(0)

4. Calculate the 2×2 determinant using the formula a*d−b*c

det(0)=(0)*(2)−(2)*(2)

det(0)=−4

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

−2⋅(−4)=8

Final Answer

det(1)=8

Want more problems? Check here!