1. Consider subsets W of a vector space V:
(a)
(b) ;
(c)

In each case determine if the given subset $W$ of a vector space $V$ is a subspace. In cases when W is a subspace of V, find a basis and the dimension of W. Justify every step of your answer.

Question

1.       Consider subsets W of a vector space V:
(a)   
(b) ;
(c)   
 
In each case determine if the given subset $W$ of a vector space $V$ is a subspace. In cases when W is a subspace of V, find a basis and the dimension of W. Justify every step of your answer.

1. Consider subsets W of a vector space V:

(a)

(b) ;

(c)

In each case determine if the given subset $W$ of a vector space $V$ is a subspace. In cases when W is a subspace of V, find a basis and the dimension of W. Justify every step of your answer.

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1. Consider subsets W of a vector space V: (a) (b) ; (c) In each case determine if the given subset $W$ of a vector space $V$ is a subspace. In cases when W is a subspace of V, find a basis and the dimension of W. Justify every step of your answer.

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1. Consider subsets W of a vector space V:

(a)

(b) ;

(c)

In each case determine if the given subset $W$ of a vector space $V$ is a subspace. In cases when W is a subspace of V, find a basis and the dimension of W. Justify every step of your answer.