Ok so my question was:(adsbygoogle = window.adsbygoogle || []).push({});

The directions state:

Find the solution space of the following systems of linear homogeneous equations:

x-y+z-w=0

2x+y-z+2w=0

2y+3z+w=0

Is the same as finding the solutions, because I did that and got (-z, -3z, 3z, z). So i said

the solution space is actually the subspace you get. For instance, this problem yields a one dimensional subspace.

---------------------------------------------------------------------------------------

And someone responded:

I don't think that solution set is right.

The vector -1,-3,3,1 does not give you 0 when used as weights in the original equation. It is a system of 4 unknowns in 3 rows there has to be a free variable somewhere. That means when you write your free variable in terms of the other variables, there should be a 0 in that solution set.

The solution (-1,-3,3,1) does not satisfy ax=0.

----------------------------------------------------------------------------------------

Am i right or am i wrong here?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Solution space to homogenous equations.

Loading...

Similar Threads for Solution space homogenous |
---|

I Solutions to equations involving linear transformations |

I Non-Hermitian wavefunctions and their solutions |

A Getting as close as possible to a solution (system of equations)? |

**Physics Forums | Science Articles, Homework Help, Discussion**