Find the Determinant [[16,6,116],[9,-5,61],[-1,7,35]]

Problem

det(16)

Solution

1. Apply cofactor expansion along the first row to set up the determinant calculation.

16*det(−5)−6*det(9)+116*det(9)

2. Calculate the 2×2 determinant for the first term.

det(−5)=(−5)*(35)−(61)*(7)

−175−427=−602

3. Calculate the 2×2 determinant for the second term.

det(9)=(9)*(35)−(61)*(−1)

315+61=376

4. Calculate the 2×2 determinant for the third term.

det(9)=(9)*(7)−(−5)*(−1)

63−5=58

5. Combine the results by multiplying each 2×2 determinant by its corresponding coefficient from the first row.

16*(−602)−6*(376)+116*(58)

6. Perform the final arithmetic to find the total value.

−9632−2256+6728

−11888+6728=−5160

Final Answer

det(16)=−5160

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