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Vectors, Subspaces and Dimensions

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2

a) Find a base for the subspace W of spanned by

What is the dimension of W?

b) Let

1) Show that W is a subspace of
2) Find a base for W
3) Determine the dimension of W

c) Let

1) Determine whether Y is a base for , the vector space of all 2 x 2 matrices.

d) Find the two values of a for which the vectors:

are linearly dependent.

In the case where a=1, express the vector in terms of

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Vectors, Subspaces and Dimensions are investigated. The solution is detailed and well presented.

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