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