(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Considering the following vectors R[tex]^{4}[/tex]:

v1 = (1,2,0,2) v2 = (2,3,1,4) v3 = (0,1,-1,0)

Determine if these vectors are linearly independent. Let S be the linear span of the three vectors. Define a basis and the dimensions of S. Express the vector v=(3,5,1,6) as a linear combination of the three vectors. Can this be achieved in a unique way? Justify your answer?

2. Relevant equations

I tried to put it into matrix form and reduce via row echolon but I'm not if this is the correct or proper way

3. The attempt at a solution

[ 1 2 0 2

2 3 1 4

0 1 -1 0

3 5 1 6]

[ 1 2 0 2

0 -1 1 0

0 1 -1 0

0 0 0 0 ]

x +2y = 2

y - z = 0

-y + 2 = 0

therefore

y=z making it linearly independent

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# Vectors Linear Independent

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