Question

Describe geometrically(line,plane or all of R^3) all linear combinations of a) (1,2,3) and (3,6,9) b) (1,0,0) and (0,2,3) c) (2,0,0) and (0,2,2) and (2,2,3)

Answer 1

a) (1,2,3)+(3,6,9)=(1,2,3)+3(1,2,3)=4(1,2,3) So all the linear combinations of these column generate multiples of (1,2,3) therefore it's a line.

Answer 2

@zepdrix Can you please help?