2 non-zero matrix A and B, and A*B=0

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The discussion centers on the relationship between two non-zero matrices A and B, where the product A*B equals zero. It establishes that if matrix C is row equivalent to A, then C*B also equals zero, as C can be expressed as C=E*A for some matrix E. This principle underscores the utility of row equivalence in solving linear systems, indicating that solutions to the equation AX=0 are also valid for CX=0. The discussion emphasizes the importance of row reduction techniques in simplifying systems for easier solution finding.

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There are 2 non-zero matrix A and B, and A*B=0.
another matrix C is a row equivalent to A.
is C*B=0 ?
 
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Yes. Because C=E*A for some matrix E.
 
actually this is the fundamental reasaon row equivalence is a useful notion in solving linear systems.

i.e. this says exactly that any solutions of the equation AX=0, also solve CX=0.

recall the use of row reduction in solving systems: you reduce A to an equivalent matrix such that CX=0 is easy to solve. then you announce that the solutions are also solutions of AX=0.
 

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