Find the Determinant (3*2)[[1,4,4],[0,-2,8],[-6,3,5]]

Problem

3⋅2*[[1,4,4],[0,−2,8],[−6,3,5]]

Solution

1. Simplify the scalar multiplier outside the matrix.

3⋅2=6

2. Set up the determinant calculation for the 3×3 matrix using expansion by minors along the first row.

det(=)*1*|[−2,8],[3,5]|−4*|[0,8],[−6,5]|+4*|[0,−2],[−6,3]|

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

|[−2,8],[3,5]|=(−2)*(5)−(8)*(3)=−10−24=−34

|[0,8],[−6,5]|=(0)*(5)−(8)*(−6)=0+48=48

|[0,−2],[−6,3]|=(0)*(3)−(−2)*(−6)=0−12=−12

4. Combine the results to find the determinant of the 3×3 matrix.

det(A)=1*(−34)−4*(48)+4*(−12)

det(A)=−34−192−48

det(A)=−274

5. Multiply the matrix determinant by the scalar factor calculated in step 1.

Total=6⋅(−274)

Total=−1644

Final Answer

3⋅2*|[1,4,4],[0,−2,8],[−6,3,5]|=−1644

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