Linear Combinations

[TCruz12]

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?

 

[pka]

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: \(\Large\vec{w}=2\vec{v_2}-\vec{v_1}\)

 

[TCruz12]

This is the simple fact: \(\Large\vec{w}=2\vec{v_2}-\vec{v_1}\)

How would you solve for a1 and a2 then?

 

[Steven G]

You start at the origin which is where the three vectors meet. Then you go from there to the tip of W. The rule is that you can only go along the blue and red lines. How would you walk from the origin to W?

BTW, pka did solve for a1 and a2.

 

[pka]

How would you solve for a1 and a2 then?

Just look at my solution!
If from that you still have questions, then you need to hire a tutor,
This is a free help site.

 

[mmm4444bot]

… If from [my reply] you still have questions, then you need to hire a tutor …

You're instructing Cruz to go somewhere else for help, if they still have questions about this exercise. You're incorrect about that, pka.

Cruz is welcome to ask as many questions here as they need.

\(\;\)

 

[yoscar04]

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.

 

[TCruz12]

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.

This helped so much thank you! I understand that a1 is 2 and a2 is -1.

 

[Dr.Peterson]

This helped so much thank you! I understand that a1 is 2 and a2 is -1.

Check that carefully. You are saying that w = a₁v₁ + a₂v₂ = 2v₁ + -1v₂. Is that correct?

 

[pka]

This helped so much thank you! I understand that a1 is 2 and a2 is -1.

In reply #2, I posted the following:

This is the simple fact: \(\Large\vec{w}=2\vec{v_2}-\vec{v_1}\)

That means \(a_2=2~\&~a_1=-1\).