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review-1 - Math 33A Spring 2008 First mid-term exam study...

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Math 33A Spring 2008 First mid-term exam study guide The first mid-term exam will cover the material from chapters 1–3 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 ( ~e 1 ), T ( ~e 2 ), . . . , T ( ~e n ), or from the values T ( ~v 1 ), T ( ~v 2 ), . . . , T ( ~v n ) for some vectors ~v i simply-related to the vectors ~e i ; 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 corre- sponding system has; Know that a function T from R m to R n

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