Describe the span of the vectors 6 7 2 3 2 4 and 4 1 2 If th

Describe the span of the vectors [-6 7 2], [3 2 4], and [4 -1 2]. If the span is a line or a plane, give the equation of the line or plane.

Solution

6.

Denote the vectors by: a, b,c

2a-b=[-15,12,0]

b-2c=[-5,4,0]

Hence,

2a-b=3(b-2c)

2a=4b-6c

ie a belongs to span of b and c

But b and c form a linearly independent set

So the span of teh vectos is span of {b,c} hwich is a plane.