Determine if w is in the subspace of R3 generated by v1 and v2

[Nemanjavuk69]

I have the following problem


Heres what I know so far. The system corresponding to $[v_1 \ v_2 \ w]$ is inconsistent, hence why $w$ is not in the subspace generated by $v_1$ and $v_1$.



My question, however, is how would one show this? Would I solve it like a system of equations and reduce to echelon form or how?

 

[Nemanjavuk69]

So I found a solution. Apparently, you try to row reduce to reduced echelon form and check if the system of equations are consistent or non consistent. In my example the system is non consistent since we have a 0=1 in the last row.

 

[Steven G]

You need to find a and b such that w = av₁ + bv₂.
If no such a and b exists then w is not in the subspace generated by v₁ and v₂

 

[Steven G]

Once you realize you want to solve w = av₁ + bv₂ you get to use any method you want that works for finding a and b or just finding out if they exist..

 

[pka]

If you know &/or understand operations with matrices, then look HERE.
How does that answer your question?