Question

Determine a base in R^4 in which the base of the subspace f is included. Base of F ((1,0,1,0)(0,1,1,1)).
Please explain.

Answer 1

is base the same as basis?

Answer 2

my thought is that since f is a subspace within R^4, then the basis for R^4 would contain f

(1,0,0,0)
(0,1,0,0)
(0,0,1,0)
(0,0,0,1)

Answer 3

yes, sorry language barrier

Answer 4

or is it saying to construct a basis for R^4 using at least the column vectors from F

Answer 5

are the f vectors orthogonal by chance?

Answer 6

yes that is what it askes

Answer 7

F1 x F2 would create a third vector that is orthogonal to the given F vectors

Answer 8

that way we would have 3 vectors and just have to find one more

Answer 9

i have a few ideas, but what are your thoughts on that matter?

Answer 10

well i think i answered yes to the wrong question, so i'll ask again, sry.
determine the basis in r^4 , including the basis of the subspace F (1,0,10)(0,1,1,1), sorry if i induced you wrong

Answer 11

ok so if i write it like ((1,0,1,0) (0,1,1,1)(0,0,0,1)(0,0,1,0)), i used the 2 vectors form the basis of F and 2 from the basis of R^4, would this be correct ?

Answer 12

real world job came calling :)

Answer 13

no problem

Answer 14

a basis consists of independant vectors, as long as the determinant of the vetor matrix is zero, that should be fine

Answer 15

http://www.wolframalpha.com/input/?i=rref%7B%7B1%2C0%2C0%2C0%7D%2C%7B0%2C1%2C0%2C0%7D%2C%7B1%2C1%2C0%2C1%7D%2C%7B0%2C1%2C1%2C0%7D%7D

when we row reduce the vectors you choose, they turn out equivalent to the R^4 basis, which means they are also independant vectors

Answer 16

so its correct, right ? because it belgons to basis of r^4

Answer 17

its correct becasue it can create all the vectors that the standard basis of R^4 creates

Answer 18

ok thank you very much for the help.

Answer 19

youre welcome