# Computation of Bases of Various Vector Spaces

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)

https://brainmass.com/math/vector-calculus/computation-bases-various-vector-spaces-475571

#### Solution Preview

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 ...

#### Solution Summary

We compute the basis of three given abstract vector spaces.

$2.19