# Let M be a matrix and u and v vectors: #M =[(a, b),(c, d)], v = [(x), (y)], u =[(w), (z)].# (a) Propose a definition for #u + v#. (b) Show that your definition obeys #Mv + Mu = M(u + v)#?

##### 1 Answer

Jul 20, 2016

Definition of addition of vectors, multiplication of a matrix by a vector and proof of distributive law are below.

#### Explanation:

For two vectors

we define an operation of addition as

Multiplication of a matrix

Analogously, multiplication of a matrix

Let's check the distributive law of such definition:

End of proof.