**UCLA, MATH 33a**

**Excerpt:** ... Math 33A Spring 2008 First mid-term exam study guide The first mid-term exam will cover the material from chapters 13 in the textbook (this includes Section 3.4, which was covered in lecture on Monday, April 21). 1 Essential notions and techniques The following is a list of essential notions you should know, and techniques you should be able to use, from the first three chapters of the textbook. Be able to solve a system of linear equations using Gauss-Jordan elimination; Be able to transform a matrix into reduced row-echelon form; Be able to multiply a matrix with a vector; Be able to find the matrix of a ** linear transformation **, given the values T (e1 ), T (e2 ), . . ., T (en ), or from the values T (v1 ), T (v2 ), . . ., T (vn ) for some vectors vi simply-related to the vectors ei ; Be able to determine the rank of an n m matrix; Know how the rank of an n m coefficient matrix relates to the number of solutions that the corresponding system has; Know that a function T from Rm to ...