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

Find a basis for the orthogonal complement of the row space of A:

A =

[1 0 2

1 1 4]

Split x = (3,3,3) into a row space component x_{r}and a nullspace component x_{n}.

3. The attempt at a solution

For the first part of the problem I took A to RREF

R =

[1 0 2

0 1 2]

and then solved to find a basis for the nullspace, x * (-2,-2,1), which should be the basis for the orthogonal complement of the row space.

I THINK that's right but maybe it's not because I'm stuck on the second part, splitting x = (3,3,3). Do I try to find a vector in Row(A) and a vector in Nul(A) that, when added, produce the vector (3,3,3)? How do I solve for that?

Help is very much appreciated!

Also, what's the best way to represent a matrix on these message boards?

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# Splitting a vector into a rowspace component and a nullspace component

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