Complete the following questions. (a) which two conditions need to be satisfied for a set of vectors in a vector space to form a subspace. (b) according to part (a), determine whether all sequences ū in roo of the form ū = (v,1,0,1,0, form a subspace.

(a) Let be a subset of a vector space . is a subspace of if and only if the following two conditions hold:

i) is closed under the sum operation. That is to say, whenever are elements of .

ii) is closed under the scalar multiplication. That is to say, whenever and

Step-by-step explanation:

For the part (b) we have the set of all sequences of the form, where . Observe the if you multiply any sequence of this form by and scalar then the sequence stops being like the given form. For example, let . Then:

This implies that the set under consideration is not closet under scalar multiplication, which implies that the set is not a subspace of the vector space of all sequences.

step-by-step explanation:

step-by-step explanation:

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