# Linear algibra - Vector space problem

• Dec 8th 2009, 12:17 AM
ddi1973
Linear algibra - Vector space problem
This is my question please give me a help to find answer

Let V be the set of ordered pairs (a, b) of real numbers. Show that V is not a vector space over \$\displaystyle \mathbb{R}\$
with vector addition and scalar multiplication defines by:
01. (a, b) + (c, d) = (a + c, b + d) and k(a, b) = (a, kb)
02. (a, b) + (c, d) = (a + c , b + d) and k (a, b) = (o , kb)
03. (a, b) + (c, d) = (ac, bd) and k(a, b) = (ka, kb)
• Dec 8th 2009, 12:38 AM
Defunkt
Where are you having diffficulties? Do you know what you should be looking at?
• Dec 8th 2009, 01:18 AM
dhammikai
Thank you very much for Ur reply,
Actually I couldn't understand this question well. Here the 03 rules are defined and then we need to prove the V is not a vector space over \$\displaystyle \mathbb{R} \$
• Dec 8th 2009, 02:55 AM
HallsofIvy
In other word, for each of the three kinds of operations defined, determine whether or not they obey the requirements for a vector space:
Addition is associative and commutative, there exist an additive identity and every element has an additive inverse, scalar multiplication is associative and commutative, and scalar multiplication distributes over addition.