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Vectors: Given z in u+v=z, find u and v (with constraints)

  • #1

Homework Statement


Given a vector z=<-12, 1, 1, 2, 7, 0> in R^6
and z=u+v, then find u and v such that u's coordinates are all equal to each other (like <0,0,0,0,0,0>) and v has coordinates that add up to 0


Homework Equations


z=u+v


The Attempt at a Solution



i have no idea how to approach this....is this a problem about direct sums? (since that is what we're studying at the moment) On a related note, what is the difference between regular addition and a direct sum?
 
Last edited:

Answers and Replies

  • #2
22,097
3,278
  • #3
What do you mean with this?
oops sorry i mean the coordinates are all equal
 
  • #4
22,097
3,278
Allright, so you want to make the following decomposition:

[tex](-12, 1, 1, 2, 7, 0)=(a,a,a,a,a,a)+(b,c,d,e,f,g)[/tex]

where b+c+d+e+f+g=0.

Now, can you derive a system of equations from this? I claim that you can obtain a system of 7 equations and 7 indeterminates (which are of course a,b,c,d,e,f,g).
 

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