Question

can (0,1) be used in a spanning set in the x and y plane?

Answer 1

there is a rule that zero vectors cannot be used in a spanning set, but is it ok to use (0,1) and (5,4) for exaple as spanning sets for the x and y plane

Answer 2

you may use (0, 1) and (1, 0)
their linear combinations fill the xy plane

Answer 3

ok so how do you solve this question then

Answer 4

you may remove the first 3 vectors

Answer 5

ok then?

Answer 6

thats it!
the vectors (-3,6) and (1,0) span R^2

Answer 7

do you get what it means to span R^2 ?

Answer 8

but you need to be careful they are not scalar multiples of eachother right?

Answer 9

like the first and second ones

Answer 10

Exactly!

Answer 11

The vectors (-3,6) and (1,0) are pointing in different directions, so they cannot be scalar multiples of each other

Answer 12

because in the answers nothing with (1,0) was mentioned, there were only three... it must be an error

Answer 13

thanks for the help!

Answer 14

np