how the rank of 3 x 3 matrix A varies with t
A= [1 1 t
1 t 1
t 1 1]

Question

how the rank of 3 x 3  matrix A varies with t 
   A=  [1   1    t
          1   t    1
           t    1   1]

zarkon · Answer

I would start by looking at the determinant.

anonymous · Answer

please help

zarkon · Answer

did you find the determinant?

anonymous · Answer

finding determinent is easy but what its use

zarkon · Answer

to start. If 

$$\det(A)\neq 0$$
then the matrix is invertible and therefore has full rank

anonymous · Answer

but  how rank varies with t

zarkon · Answer

There will be a couple values of t that make det(A)=0.  then the rank will not be 3

zarkon · Answer

$$\det(A)=-(t-1)^2(t+2)$$

and therefore det(A) =0 at t=1 and -2

1 is a root of order 2 so the rank of the matrix will only be 1

-2 is a root of order 1 so the rank of the matrix will be 2

for all other values of t the rank is 3

zarkon · Answer

you understand?

anonymous · Answer

yes thanks