MathProblemsBank

1.9.3 Linear spaces

Problem: Find out, does the set of all real numbers forms the linear space if the sum of any two elements \( a \) and \( b \) is defined in it, equal to \( a+b \) and the product of any element \( a \) by any real number \( \varepsilon \), equal to \( \varepsilon \cdot a \).