Question

under what conditions on the scalar x do the vectors (0,1,x) , (x,0,1), (x,1,1+x) form a basis of C^3?

Answer 1

Are we sure that it's possible for them to? The third vector is the sum of the first two vectors, so I don't see how they could be independent?

Answer 2

that's what i thought ! it's a project but i don't know if my teacher would ask a trick question

Answer 3

Never, because they are not independent whatever the value of x. Calculate the determinant and will see the result is 0. Is also easy to see that the 3rd vector, for instance, is the first vector plus the second

Answer 4

ok thank you so much:)