Suppose cu = 0 for some nonzero scalar c. Show that u = 0. Mention the axioms or properties you use.
Step 1 of 2
Consider for some nonzero scalar c,
Need to show that,
Suppose a non-empty set of vectors, V is a vector space. Then, the following axioms must hold for all vectors in V, and, for all scalars, and, .
If are in V, then, the sum of denoted by, is in V.
, where zero 0, is a vector in V.
For each in V, there exists a vectorin V, such that
For in V, and, for a scalar, the scalar multiple of by, is denoted by , is in.