A Book of Abstract Algebra

Charles C. Pinter

Chapter 28 VECTOR SPACES - all with Video Answers

Educators

Section 1

Problem 1

Prove that $\mathbb{R}^{n}$, as defined on page 283 , satisfies all the conditions for being a vector space over $\mathbb{R}$.

Donald Albin

Numerade Educator

01:19

Problem 2

Prove that $\mathscr{F}(\mathbb{R})$, as defined on page 284 is a vector space over $\mathbb{R}$.

Monica Miller

Numerade Educator

01:19

Problem 3

Prove that $\mathscr{P} \ell$, as defined on page 284 , is a vector space over $\mathbb{R}$.

Monica Miller

Numerade Educator

01:48

Prove that $\|_{2}(R)$, the set of all $2 \times 2$ matrices of real numbers, with matrix addition and the scalar multiplication
$$
k\left(\begin{array}{ll}
a & b \\
c & d
\end{array}\right)=\left(\begin{array}{ll}
k a & k b \\
k c & k d
\end{array}\right)
$$
is a vector space over $\mathbb{R}$.

Manik Pulyani

Numerade Educator

Problem 1

Problem 2

Problem 3

Problem 4