Answer to Question #265702 in Linear Algebra for Almas

Question

Prove that a scalar and vector can be added.

Answer 1

Any set can be added if it satisfies the conditions and norms of addition.

The norm gives an accurate closure to adding things. Vectors and scalars are closed under addition because they satisfies the following axiom.

1) Commutative property

$A+B=B+A$

2) Associative Property

$x+(y+z)=(x+y)+z$

3) Distributive Property

$A×(B+C)=A×B+A×C$

4) Additive Identity Property

$A+0=A$