Hello everyone,(adsbygoogle = window.adsbygoogle || []).push({});

it's final's time next week , so I will be posting here more often than usual

Here is one problem I came across when doing review:

The nullspace of non-zero 4x4 matrix cannot contain a set of 4 lin. indep. vectors. (T/F)

The way I was thinking is that if I solve a homogeneous s-m with this matrix, and if the dimension of nullspace is 4, that means that there have to be 4 free variables in the homogeneous s-m, but matrix is just 4x4.

And then there is this rank-nullity theorem thatn = rank(A) + nullity(A), so in this case rank(A) = 0, is it ever possible? My guess is not.

Does the same hold for dim of nullspace (nullity): it has to have at least one solution (trivial, where everyting = 0, but that does not mean that the nullity is an empty set!) ?

Is it correct?

Thanks in advance!

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

Join Physics Forums Today!

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

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

# Nullspace of non-zero 4x4 matrix

Loading...

Similar Threads for Nullspace zero matrix |
---|

I Eigenproblem for non-normal matrix |

A Eigenvalues and matrix entries |

A Badly Scaled Problem |

I Adding a matrix and a scalar. |

I Getting a matrix into row-echelon form, with zero-value pivots |

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