Question

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

Answer 1

I would start by looking at the determinant.

Answer 2

please help

Answer 3

did you find the determinant?

Answer 4

finding determinent is easy but what its use

Answer 5

to start. If

\[\det(A)\neq 0\]
then the matrix is invertible and therefore has full rank

Answer 6

but how rank varies with t

Answer 7

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

Answer 8

\[\det(A)=-(t-1)^2(t+2)\]

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

Answer 9

you understand?

Answer 10

yes thanks