Question

S = { (1,2,3), (4,5,6), (11,16,21) }
Does the vector (6,9,12) \[\in\] span{S}

Answer 1

I solved the matrix:
x y z b
[ 1 4 11 | 6 ]
[ 2 5 16 | 9 ]
[ 3 6 21 | 12]

Answer 2

You can eyeball it

Answer 3

and got x=2-3z, y=1-2z and z in R

Answer 4

What do those answers tell me?

Answer 5

that tells you that you can reach the vector (6, 9, 12) by taking linear combinations of the given vectors

Answer 6

-(1,2,3)-(4,5,6)+(11,16,21) = (6,9,12)

Answer 7

The moment you said to eyeball it, i immediately noticed that.

Answer 8

they cook up these examples precicely for eyeballing

Answer 9

Next time i'll take a look before solving like crazy, thanks ganeshie8

Answer 10

np :)