*8*

*Matrices and vector spaces*

**8.1***Which of the following statements about linear vector spaces are true*? *Where* *a statement is false, give a counter-example to demonstrate this.*

(a) *Non-singular N* × *N matrices form a vector space of dimension N*^{2}.

(b) *Singular N* × *N matrices form a vector space of dimension N*^{2}.

(c) *Complex numbers form a vector space of dimension* 2.

(d) *Polynomial functions of x form an infinite-dimensional vector space.*

(e) *Series* {*a*_{0}*, a*_{1}*, a*_{2}*, . . . , a _{N}*}

(f) *Absolutely convergent ...*

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