MATH125 Lecture Notes - Lecture 8: Invertible Matrix, Null Character, Scalar Multiplication

• School: University of Alberta
• Department: Mathematics
• Course: MATH125
• Professor: Vladimir Chernousov

Document Summary

Subspaces, basis, dimension, and rank 50% of the final. The vectors that make up l also live on the line l. If we take two vectors from the line, then their sum also exists on the line. This is not the case for curved lines. Also, this line contains the zero vector and is more symmetric than a curved line. Definition: a subset h in rr is called a (vector) subspace if it has the following properties: It contains the zero vector (it passes through the origin) If u and v are vectors in h, their sum is also contained in h: for every u in h and every scalar c in rn, the scalar product cu is contained in h. In words: h contains 0 and is stable with respect to addition and scalar multiplication. Example: let u,v be vectors in rn then the span(u,v) is a subspace.