This is the simple fact: \(\Large\vec{w}=2\vec{v_2}-\vec{v_1}\)View attachment 20677
I'm having trouble understanding how get the value of "w" to know if you can write it as a linear combination? Could I get some explanation on how to get that value to complete the problem?
This is the simple fact: \(\Large\vec{w}=2\vec{v_2}-\vec{v_1}\)
Just look at my solution!How would you solve for a1 and a2 then?
You're instructing Cruz to go somewhere else for help, if they still have questions about this exercise. You're incorrect about that, pka.… If from [my reply] you still have questions, then you need to hire a tutor …
The question tells you that [MATH]\vec{w}[/MATH]=a1[MATH]\vec{v}[/MATH]1+a2[MATH]\vec{v}[/MATH]2 and pka wrote: also that [MATH]\vec{w}[/MATH]=2[MATH]\vec{v}[/MATH]2-[MATH]\vec{v}[/MATH]1. There are two issues here: first that you agree with what pka wrote in his first reply. After that, check that you can identify a1 and a2. I hope that helps you.How would you solve for a1 and a2 then?
The question tells you that [MATH]\vec{w}[/MATH]=a1[MATH]\vec{v}[/MATH]1+a2[MATH]\vec{v}[/MATH]2 and pka wrote: also that [MATH]\vec{w}[/MATH]=2[MATH]\vec{v}[/MATH]2-[MATH]\vec{v}[/MATH]1. There are two issues here: first that you agree with what pka wrote in his first reply. After that, check that you can identify a1 and a2. I hope that helps you.
Check that carefully. You are saying that w = a1v1 + a2v2 = 2v1 + -1v2. Is that correct?This helped so much thank you! I understand that a1 is 2 and a2 is -1.
In reply #2, I posted the following:This helped so much thank you! I understand that a1 is 2 and a2 is -1.
That means \(a_2=2~\&~a_1=-1\).This is the simple fact: \(\Large\vec{w}=2\vec{v_2}-\vec{v_1}\)