Chapter 6.2, Problem 55E

Identify the zero element and standard basis for each of the isomorphic vector spaces in Example $12$.

EXAMPLE $12$ Isomorphic Vector spaces

The vector spaces below are isomorphic to each other.

a. $R^4=4-\text{space}$

b. $M_{4,1}=\text{space}\text{of}\text{all}4\times 1\text{matrices}$

c. $M_{2,2}=\text{space}\text{of}\text{all}2\times 2\text{matrices}$

d. $P_3=\text{space}\text{of}\text{all}\text{polynomials}\text{of}\text{degree}3\text{or}\text{less}$

e. $V=\left\{\left(x_1,x_2,x_3,x_4,0\right):x_i\text{is}\text{a}\text{real}\text{number}\right\}$ (subspace of $R^5$)