Jump to content

System of linear equations/Set of variables/Equivalent system/Manipulations/Fact/Proof

From Wikiversity
Proof

Most statements are immediately clear. (2) follows from the fact that if

holds, then also

holds for every . If , then this implication can be reversed by multiplication with .

(6). Let be the equation

and be the equation

If a tuple satisfies both equations, then it also satisfies the equation . And if the tuple satisfies the equations and , then it also satisfies the equation and .