Question

Does S={(1,-1)(2,1) span R^2?

Answer 1

use elimination to see if there are 2 pivots

Answer 2

elimination? how?

Answer 3

What do u mean?

Answer 4

I'm curious, is this linear algebra or multi at your school?

Answer 5

my textbook never explained it to us using that method

Answer 6

linear algebra

Answer 7

neways i wld say that it does span R^2

Answer 8

In that case you must show that all linear combinations of (1,-1)(2,1) correspond to all linear combinations reached by (1,0), (0,1)
or
a matrix made of these vectors has a non-zero determinant

Answer 9

or show they are not dependent (fall on the same line)

Answer 10

ok got it so i was correct then?

Answer 11

Definitely spans R^2, by the picture, you see you can reach any point by moving some distance (plus or minus) along one vector, and then some distance along the second vector.

Answer 12

ok i think i get it

Answer 13

so i guess S={(0,2)(1,4) also spans R^2

Answer 14

yep

Answer 15

ok so basically if the points are like a multiple of another then it wld form a line so it wldnt span R^2

Answer 16

if they can be reduced to the identity matrix/ if they are linearly independent/ if they form a matrix with a non-zero determinant
they span R2

all those above things imply each other

Answer 17

(1,0) and (0,1) span R2, right?

Answer 18

kk i got it thanks.

Answer 19

if you think of them in a linear combination you get the above matrix, which you can see has a non-zero determinant