# vector spaces

Briefly explain, which of the following are vector spaces?

(a) The set of all real symmetric 3x3 matrices.

(b) The set of all real 3x3 non-singular matrices.

(c) The set of all real functions f(x) which are continuous for all x.

https://brainmass.com/math/vector-calculus/identify-vector-spaces-364168

#### Solution Preview

(a) The sum of two symmetric matrices and the scalar multiple of a symmetric matrix is again a symmetric matrix. The zero matrix is ...

#### Solution Summary

Vector spaces are clearly evaluated in this solution.

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