Which ones of the following subsets of are subspaces.
a)
b)
c)
d)
I should decide their dimensions and give a basis for each. I think a) and d) are subspaces, how can I find the dimension of these spaces and how can I give a basis?
Thank you!
I did it this way. So when the linear combination of 2 random elements of the set gives an element which in the set too, it is a subspace.
For c) the 0-vector isn't in the set so it cannot be a subspace.
For d) I did the same what you did with a). It is a subspace.
For b) I got from the lin.comb of 2 elements (a+b)*c when c is the constant and a,b are scalars, so I think I should have got c, so it is not a subspace.
But my main problem is I cannot decide their dimensions and cannot give a basis