Find the Determinant v=[[i,j,k],[-1,0,5],[9,-4,-2]]

Problem

det(i)

Solution

1. Apply cofactor expansion along the first row to break the 3×3 determinant into 2×2 determinants.

2. Set up the first term by multiplying the element i by the determinant of the matrix remaining after removing the first row and first column.

i*det(0)

3. Set up the second term by multiplying the element j by the negative of the determinant of the matrix remaining after removing the first row and second column.

−j*det(−1)

4. Set up the third term by multiplying the element k by the determinant of the matrix remaining after removing the first row and third column.

k*det(−1)

5. Calculate the 2×2 determinants using the formula det(a)=a*d−b*c

i*((0)*(−2)−(5)*(−4))−j*((−1)*(−2)−(5)*(9))+k*((−1)*(−4)−(0)*(9))

6. Simplify the arithmetic inside each set of parentheses.

i*(0+20)−j*(2−45)+k*(4−0)

7. Combine the terms to find the final vector expression.

20*i+43*j+4*k

Final Answer

det(i)=20*i+43*j+4*k

Want more problems? Check here!