SOLUTION: Let v1=[2,0,6] , v2=[-1,4,5] , v3=[1,-1,1]. Find the value(s) of k for which b=[2,1,k] can be written as a linear combination of vectors v1, v2, and v3. My attempt: c1v1 + c2

Question 1086854: Let v1=[2,0,6] , v2=[-1,4,5] , v3=[1,-1,1].
Find the value(s) of k for which b=[2,1,k] can be written as a linear combination of vectors v1, v2, and v3.
My attempt:
c1v1 + c2v2 + c3v3 = b.
[[2 -1 1 | 2]
[0 4 -1 | 1]
[6 5 1 | k]]
I simplified this matrix down to:
[[1 -1/2 1/2 | 1]
[0 1 -1/4 | 1/4]
[0 0 0 | k-8 ]]
I got stuck at this part. I was not sure what to do after this or whether I was approaching the problem properly.
Answer by ikleyn(52786) (Show Source): You can put this solution on YOUR website!
.
From your result, it follows k = 8.

It can not be nothing else.

RELATED QUESTIONS
1)In 3d-space, let v1=(0,2,1) v2=(2,1,1) v3=(1,3,-1) v4=(4,2,1). Write v4 as linear... (answered by Fombitz)

The vector v=[4 5] can be written as a linear combination of the vectors v1=[1 3]... (answered by Edwin McCravy)

Let S={v1, v2, v3}where v1^T=[1 0] v2^T=[0 1] v3^T=[-1 1] (answered by venugopalramana)

hello How do i find the basis of a space spanned by a set of vectors v1 =... (answered by Jk22)

I have a homework problem that I don't know how to do. I'm asked to solve the following (answered by venugopalramana)

Let A: [v1 v2 v3] with v1=(1,-1,0)T, v2=(2,0,-2)T and v3=(3, -3,3)T a) Show that... (answered by rothauserc)

Let v1=(1,6,4), v2=(2,4,-1), v3=(-1,2,5) and w1=(1,-2,-5), w2=(0,8,9). Prove that... (answered by khwang)

Last month, Jacob traveled from Miami to New Orleans by train and made two stops along... (answered by solver91311)

Last month, Jacob traveled from Miami to New Orleans by train and made two stops along... (answered by robertb)