I have a quick question regarding matrix equations. Usually, I would look this up but unfortunately I'm away from the office and library and it can't wait until I get back.(adsbygoogle = window.adsbygoogle || []).push({});

Let [itex]A_1[/itex] and [itex]A_2[/itex] be [itex]n\times n[/itex] square matrices with real elements and let [itex]\boldsymbol{x}_1\;,\boldsymbol{x}_2\in\mathbb{R}^n[/itex]. Further, let [itex]A_1 \boldsymbol{x}_1 = \boldsymbol{0}[/itex]. What is the solvability condition for the following system?

[tex]A_1\boldsymbol{x}_2 = A_2\boldsymbol{x}_1[/tex]

The result would suggest [itex]\boldsymbol{x}_1^\text{T}A_2\boldsymbol{x}_1 = 0[/itex], but I'm clearly missing something. I fairly certain its something minor that I just can't see.

Any help would be very much appreciated.

**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!

# Matrix Equation

Loading...

Similar Threads - Matrix Equation | Date |
---|---|

I Matrix Equation -- clarification about solving a system | Aug 1, 2017 |

I Can this matrix equation be solved? | May 30, 2017 |

I Factorization of a matrix equation | Oct 20, 2016 |

I Solving equations with singular matrix | Jul 26, 2016 |

Reduction of matrix equation | Dec 2, 2015 |

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