Suppose A and B are matrices of the same size, and x is a column vector such that the matrix products Ax and Bx are defined.(adsbygoogle = window.adsbygoogle || []).push({});

Suppose that Ax=Bx for all x. Then is it true that A=B?

I know that this is true and I can prove it using the idea of transformation matrices, and viewing Ax and Bx each as linear transformations and showing that those two transformations are equivalent, but I was curious if this can be proved without appealing to the notion of a linear transformation.

Tips?

BiP

**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!

# Ax=Bx for all x implies A=B

Loading...

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

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 |

The nonhomogenous system Ax=b | May 28, 2013 |

Guarantee Ax=Bx implies A=B? | Oct 2, 2005 |

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