Thread: linear

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 ?

Yes. Because C=E*A for some matrix E.

actually this is the fundamental reason 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.