Find the Determinant

Problem

det(1)

Solution

1. Use row operations to create zeros in the first column. Add 3 times the first row to the second row ((R_2)+3*(R_1), subtract 3 times the first row from the third row ((R_3)−3*(R_1), and add the first row to the fourth row ((R_4)+(R_1).

det(1)

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

1⋅det(−6)

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

−4⋅det(−6)

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

det(−6)=(−6)*(−4)−(4)*(7)

det(−6)=24−28=−4

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

−4⋅(−4)=16

Final Answer

det(1)=16

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