For the question show that the determinant is a negative integer - Maths - Determinants

Question

For the question show that the determinant is a negative integer

Vijay Kumar Gupta · Accepted Answer

Dear student,

Consider the follwoing determinant               ∆=x-22x-12x2x-12x2x+12x2x+12x+22                  =x-22x2x+22-x+12x+12-x-12x-12x+22-x+12x2+x2x-12x+12-x2x2                  =x2-4x+4x2x2+4+4x-x2+2x+1x2+2x+1-x2-2x+1x2-2x+1x2+4x+4-x2+2x+1x2+x2x2-2x+1x2+2x+1-x4                  =-2x4-4x3-x2+8x3+16x2+4x-8x2-16x-4--4x4-4x3+4x2+8x3+8x2-8x-4x2-4x+4-2x4+x2                  =-2x4-4x3-x2+8x3+16x2+4x-8x2-16x-4+4x4+4x3-4x2-8x3-8x2+8x+4x2+4x-4-2x4+x2                  =-4x4+4x4-4x3+4x3+8x3-8x3-x2+x2+16x2-16x2+16x-16x-8                  =-8Thus, on solving the above determinant, we get  negative integer as -8
Regards