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Computation of Bases of Various Vector Spaces

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For each of the following vector spaces, give its dimension and a basis.

(a) the set of all symmetric 4 x 4 matrices,
(b) the subspace of P3 consisting of those polynomials in P3 whose graphs
pass through the origin
(c) the set of all vectors in R3 that are orthogonal to v = (1,2,-1)

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Solution Summary

We compute the basis of three given abstract vector spaces.

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For each of the following vector spaces V, we wish to give its dimensions and find a basis.
(a) The set of all symmetric matrices.
Every symmetric matrix can be written in the following form:

where are arbitrary ...

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