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

The set of vectorsu= {1,-2,2,1},v= {1,3,1,1},w= {3,4,4,3} cannot span R4. Complete this set to create a set of vectors that will span R4. Show that your set of vectors spans R4.

3. The attempt at a solution

Let [tex]y = {y_1,y_2,y_3,y_4}[/tex]. I write span{u,v,w,y} as the coefficient matrix:

[1,1,3,y_1

-2,3,4,y_2

2,1,4,y_3

1,1,3,y_4]

Using the first row to produce zeros in each row below yields:

[1,1,3,y_1

0,5,10,y_2+2y_1

0,-1,-2,y_3-2y_1

0,0,0,y_4-y_1]

Using the second row to produce zeros in the row below yields:

[1,1,3,y_1

0,5,10,y_2+2y_1

0,0,0,5y_3-9y_2+2y_1

0,0,0,y_4-y_1]

So to my understanding, it would seem given the set {u,v,w}, a fourth vectorycannot be chosen so that the set {u,v,w,y} spans R4 since not every row can contain a pivot position in this case. Please correct me if I am wrong.

- Sam

PS sorry for the messy work - I don't know how to write matrices in latex.

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# For a set of vectors to span R4 question

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