Question

In any vector space au=bu implies a=b ? Trou or False​

Answer 1

Answer:

False

Explanation:

(I guess if it were written "properly" it would be ax=bx implies a=b).

Given the axioms we were given, it would seem that the statement should be true, no?

A related statement -- also listed as false -- is that "in any vector space, ax=ay implies that x=y." Again, given the axioms we have.

Answer 2

Answer:

False

Explanation:

Simply use the counterexample u = 0

For zero vector:

au=bu=0

holds for a=3, b=4

False