Find the Determinant [[x,4,x^2],[6,-x,0],[-1,x^3,1]]

Problem

det(x)

Solution

1. Apply cofactor expansion along the second row to simplify the calculation, as it contains a zero.

2. Calculate the first term by multiplying the element 6 by its cofactor, noting the sign change for position (2,1)

−6⋅det(4)=−6*(4*(1)−x(x3)2)

−6*(4−x5)=−24+6*x5

3. Calculate the second term by multiplying the element −x by its cofactor, keeping the positive sign for position (2,2)

+(−x)⋅det(x)=−x*(x(1)−x2*(−1))

−x*(x+x2)=−x2−x3

4. Combine the results from the expansion to find the final polynomial expression.

6*x5−24−x3−x2

Final Answer

det(x)=6*x5−x3−x2−24

Want more problems? Check here!