Given nxn matrices A and B, and an n-vector x, are there any conditions that can guarantee Ax=Bx implies A=B? I started thinking about this well working on an assignment. It is clearly not always true, since you can easily think up 2x2 examples where it is not. You can also think up examples where the determinants are non-zero, and not equal to each other, where it still doesnt hold. What conditions if any would make this implication true? Thank you.(adsbygoogle = window.adsbygoogle || []).push({});

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

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

# Guarantee Ax=Bx implies A=B?

Loading...

Similar Threads - Guarantee Ax=Bx implies | Date |
---|---|

B ##AB = I \implies BA = I##, for square matricies ##A,B## | Jun 9, 2017 |

How to find basis vectors for a+ ax^2+bx^4? | Feb 17, 2016 |

Jordan Chains to solve x'=Ax, complex-valued. | Feb 8, 2016 |

Ax=b Gauss elimination or? | Jul 26, 2013 |

Ax=Bx for all x implies A=B | Jun 17, 2013 |

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