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.

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# Matrix Equation

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