A generalization to other mathematical objects. We are extending the properties of vectors that we have been studying to functions, matrices, equations, infinite sequences and other objects.

A linear space V is a set that is closed under addition, closed under multiplication, and satisfies the 8 rules on p. 153.

To find a basis for a linear space V: write dow a typical elemet of V, in terms of some arbitrary constants; use the arbitrary constants as coefficients to express your typical element as a linear combination of some elements of V; verify that the elements of V in this linear combination are linearly independent.

Section 4.1 - 1, 3, 7, 9, 11, 13, 21, 27, 35, 47