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Solution to Linear Algebra Done Wrong Exercise 1.1.2

Which of the following sets (with natural addition and multiplication by a scalar) are vector spaces. Justify your answer.

a) The set of all continuous functions on the interval $[0, 1]$;
b) The set of all non-negative functions on the interval $[0, 1]$;
c) The set of all polynomials of degree exactly $n$;
d) The set of all symmetric $n\times n$ matrices, i.e. the set of matrices $A =(a_{j,k})^n_{j,k=1}$ such that $A^T = A$. (more…)

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