Plz help me. I can't google about reduce or expand vector space

[hahalalamummy]

Reduce each of following sets of vector to oblain a basis for the given vector space
p₀=2, p₁=-4t, p₂=1+t+t^2, p₃=7+2t, p₄=-1+5t^2 in P₂


Expand each of following sets of vector into a basis for the given vector space
v₁={{15;0},{0;0}} and v₂={{2;-1},{0;0}} in M₂
Thank guy

 

[HallsofIvy]

Reduce each of following sets of vector to oblain a basis for the given vector space
p₀=2, p₁=-4t, p₂=1+t+t^2, p₃=7+2t, p₄=-1+5t^2 in P₂

_{This looks fairly straightforward. What have you done on it? What properties must a basis have?}

Expand each of following sets of vector into a basis for the given vector space
v₁={{15;0},{0;0}} and v₂={{2;-1},{0;0}} in M₂
Thank guy

What, exactly is "M₂"? What is its dimension? And what properties must a basis have?

 

[hahalalamummy]

This looks fairly straightforward. What have you done on it? What properties must a basis have?


What, exactly is "M₂"? What is its dimension? And what properties must a basis have?

This is my homework teacher gave me. I only know P₂ is like at^2+bt+c and M₂ is matrix 2*2.

 

[HallsofIvy]

Obviously, your teacher expects you to know what "vector space" and "basis" mean! If you do, tell us what you understand by them so we can correct you if necessary and give you meaningful help. If you don't, then look them up.

 

[hahalalamummy]

Obviously, your teacher expects you to know what "vector space" and "basis" mean! If you do, tell us what you understand by them so we can correct you if necessary and give you meaningful help. If you don't, then look them up.

Of course i understand that. What I don't understand is why should reduce P₂ space to P₂ space and expand M₂ to it self?

 

[Steven G]

Here is a hint. 2=2 + 0t + 0t^2. Since P2 ~ R^3 we should think of 2 as the vector (2,0,0) in R^3. So you can easily get 4 vectors in R^3 from what you were given. So how do you go from these 4 vectors in R^3 to a basis in R^3? Then rewrite this basis in R^3 to vectors (or polynomials) in P2.