Recent content by gotmejerry

a(1+t+t2) + b(1-t2) = c(1-t+t2) + d(3+2t+t2) is true if a-b=c+d a=2d-c a+b=c+3d What do I do now?

1. If I take the linear combinations of p1 p2 q1 q2 as I have written and I am not wrong I think the basis {t^2 t 1} is ok. 2. I found out that {p1,p2} and {q1,q2} are linearly independent, because a*p1+b*p2=0 s only solution is the trivial soulution, same for {q1,q2}. So dim(M)=2 and...

Homework Statement Let M be a subspace of the vector space \mathbb{R}_2[t] generated by p_1(T)=t^2+t+1 and p_2(T)=1-t^2, and N be a subspace generated by q_1(T)=t^2+2t+3 and q_2(T)=t^2-t+1. Show the dimension of the following subspaces: M+N, M \cap N, and give a basis for each...

Let K1={a + (2^0.5)*b} | a,b rational numbers}, and K2={a + (3^0.5)*b} | a,b rational numbers} be two fields with the common multiplication and addition. Isomorphs are the following vector spaces : (Q^n ., +; K1) and (Q^n ., +; K2) ?

But I maybe got the definition wrong.

I guess I know. I wrote 3 equations: α + 2β + Lγ = 0 α + Lβ + 2γ = 0 α + + 3γ = 0 And i got, L can be 1 or 2. Then I checked it and for these Ls the vectors are dependents. But how do I know that there aren't more Ls. For the second question. Yes L is from those values.

So i have 3 vectors: a= [1 1 1] b= [2 L 0] c= [L 2 3] How do I calculate the L in order to make these vecotrs linearly dependent? How does ß depend from L if v= [ß 0 -1] and v is in span(a b c)? Thank you!

I can see why it is need to be true, when I draw it, unfotunately I cannot write down the solution in a mathematical way.

Homework Statement How can I prove this? If g°f is a bijective function, then g is surjective and f is injective. Homework Equations The Attempt at a Solution