Question

For which real numbers x do the vectors: (x, 1, 1, 1), (1, x, 1, 1), (1, 1, x, 1), (1, 1, 1, x)
not form a basis of R
4
? For each of the values of x that you find, what is the dimension
of the subspace of R
4
that they span?

Answer 1

(4,1,1,1),(1,4,1,1),(1,1,4,1),(1,1,1,4) do form a basis, because the four vectors are linearly independent.
(1,1,1,1),(1,1,1,1),(1,1,1,1),(1,1,1,1) do not.
The rank of R with x=1 is obviously 1, since all the vectors are identical.

Answer 2

thanks....

Answer 3

You're Welcome!