Describing Points in Configurations using Set Theoretic and Vector Notation

[babbagee]

I am having a hard time with this problem, and i need some help.

It says:
In Exercisies 11-17, use set theoretic or vector notation or both to describe the points that lie in the given configurations.

11.) The plane spanned by v₁ = (2,7,0) and v₂ = (0,2,7)

In the back of the book they have this answer
{(2s,7s+2t,7t)| sER, tER}

I know all they did was add the two vectors together, but i don't know how the got s, and t and what they represent.

E= is a member of

 

[master_coda]

A vector is in the span of v1 and v2 if and only if it is a linear combination of v1 and v2. In other words, v is in the span if

$$\boldsymbol{v}=s\boldsymbol{v}_1+t\boldsymbol{v}_2$$

where s and t are any two real numbers. This is pretty much what the set theory notation is saying.


Perhaps I didn't explain this too well. I'm not sure what your level of knowledge is, so I don't know how in-depth you need me to go.

 

[HallsofIvy]

Looks good to me master_coda.

Rajvirnijjar, perhaps you should review the concept of "spanning".