In any vector space $V$, show that $(a+b)(x+y)=a x+a y+b x+b y$ for any $x, y \in \mathrm{V}$ and any $a, b \in F$.

By \texttt{VS-7} and \texttt{VS-8}, we have $$(a+b)(x+y)=a(x+y)+b(x+y)=ax+ay+bx+by.$$

Exercise 1.2.8

In any vector space $V$ , show that $(a + b) (x + y) = ax + ay + bx + by$ for any $x, y \in V$ and any $a, b \in F$ .

By VS-7 and VS-8, we have

(a + b) (x + y) = a (x + y) + b (x + y) = ax + ay + bx + by .

jephianlin

2011-06-27 00:00