Given the matrix A defined by Using what you know about the

Given the matrix A defined by: Using what you know about the determinant, find all values of x for which there is a nontrivial nullspace null(A). Think about what the determinant tells you about the dependence or independence of your equation system.

Solution

If the Determinant is zero then the system is linearly dependent and linearly independent if

determinant is non zero

DetA : (2-x)(-x)(5-x) =0

x =0 ; x =2 ; x= 5

So, for x = 0, 2 , 5 system is linearly dependent