This is linear Algebra question Please prove it that For any

This is linear Algebra question. Please prove it that \"For any p which is not equals to -1 is linearly independent set\"

Solution

Calcualte the determinant of the given vectors after expressing them in matrix form.

[1 3 p
0 2 1
-1 p 2]
Its determinant will be 1(4-p)- 3(0+1) + p (0+2) = 4-p-3+2p = p+1;

if it is a lineraly independent set then determinant vaue should not be equal to zero.

That is p+1 should not be equal to zero which means p should not be -1;

Hence proved