This is the first time I'm posting (or rather asking) anything here. I'm a student of elementary linear algebra, therefore plz excuse me if my questions come across as dumb or if I make any mistakes:(adsbygoogle = window.adsbygoogle || []).push({});

I have a question about determinants and whether or not a solution exists, etc. I will be focusing on square matrices only:

If the determinant of a matrix is not equal to zero, then does that mean the matrix has a unique solution?

If the determinant is equal to zero, then either the matrix has infinitely many solutions or no solution, correct?

And if it is a homogeneous system, then the system has infinitely many solutions if the determinant is equal to zero, correct?

Thanking you in advance,

Bye.

P.S. Could someone kindly tell me what is meant by singular and non-singular matrices?

**Physics Forums - The Fusion of Science and Community**

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!

# Square matrices, determinants and consistency

Loading...

Similar Threads for Square matrices determinants | Date |
---|---|

Fair to say there are twice as many square matrices as rectangular? | Apr 10, 2013 |

Non-square matrices and inverses | Dec 1, 2012 |

Transforming between square matrices of different order | Aug 28, 2012 |

Solbing equation A(u)=B(v) for square matrices A and B | Apr 1, 2012 |

Linear dependence of square matrices | Feb 10, 2011 |

**Physics Forums - The Fusion of Science and Community**