Calculating Linear Span: Vector a1 (-7, 8, 5) and Line Equation

[dracolnyte]

Homework Statement

(i)Show that the linear span of the vector a1 = (-7, 8, 5) is the line whose equation is
x/(-7) = y/8 = z/5

The Attempt at a Solution

The problem is, I don't know where or how to start.

 

[Dick]

Define the 'linear span of a vector'. Look it up if you have to.

 

[dracolnyte]

The linear span of a vector is the collection of all linear combinations of the vectors a1, a2..., ak

 

[Dick]

Ok, so for one vector v1 it's the set of all vectors k*v1 for k any real number, right?

 

[dracolnyte]

Ya, and then?

 

[Dick]

You are supposed to be helping here. Guess. (x,y,z) is a point in the span of (-7, 8, 5). What's it equal to?

 

[dracolnyte]

Okay so
-7k = x
8k = y
5k = z

 

[dracolnyte]

Got it, thank you so much. I'll be back with more for sure lol.