Help me to find answers for these linear algebra questios

[priyan thushara]

1). let V be set of ordered pairs (a,b) of real numbers. show that V is not a vector space over R with addition and multiplication defined by
a) (a,b)+(c,d)=(a+d,b+c) and k(a,b)=(ka,kb)
b) (a,b)+(c,d)=(0,0) and k(a,b)=(ka,kb)
c) (a,b)+(c,d)=(ac,bd) and k(a,b)=(ka,kb)

2). let V be the vector space of n-square matrices over a field K. show that W is a subspace of V if W consist of all matrices A=[A_ij] that are
a) symmetric (A^T=A)
b) diagonal

 

[Deleted member 4993]

1). let V be set of ordered pairs (a,b) of real numbers. show that V is not a vector space over R with addition and multiplication defined by
a) (a,b)+(c,d)=(a+d,b+c) and k(a,b)=(ka,kb)
b) (a,b)+(c,d)=(0,0) and k(a,b)=(ka,kb)
c) (a,b)+(c,d)=(ac,bd) and k(a,b)=(ka,kb) <<< Is that correct?

2). let V be the vector space of n-square matrices over a field K. show that W is a subspace of V if W consist of all matrices A=[A_ij] that are
a) symmetric (A^T=A)
b) diagonal

.

 

[priyan thushara]

solve above questions

I can't solve above linear algebraic questions that's why i post here that questions. please help me to find answers.

 

[tkhunny]

What is your question?
Did you read "Read before posting"?

If you are in the right class, you probably are to find the answer in your head. Think, ponder, agonize, and come up with something. Unless you've done some of those three, or are at least willing to do so, this is as far as you will get in your mathematical career.


So, show us what you have done and we can help you take some helpful next step. Seriously, show SOMETHING. You can't have NO idea. That is just not acceptable.