Problem 30E

Suppose cu = 0 for some nonzero scalar c. Show that u = 0. Mention the axioms or properties you use.

Solution 30E

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.