This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math 136 Sample Term Test 1 NOTES:  Questions 4d, 5, 6 on this test cover material that will not be covered on our term test 1. Students had 90 minutes to write this test, where you will have 110 minutes. 1. Short Answer Problems a) List the 3 elementary row operations. b) Does the spanning set span { (1 , 2 , 1) , (0 , 1 , 0) , (1 , , 1) } represent a line or a plane in R 3 ? Give a vector equation which describes it. c) What is the area of the parallelogram induced by ~a = (2 , 3) and ~ b = (1 , 1). d) If A is an n × m matrix and B is an m × p matrix, then what is the size of AB ? e) Explain why ~a × ( ~ b × ~ c ) must be a vector in the plane with vector equation ~x = s ~ b + t~ c , s,t ∈ R . 2. Consider the system of linear equations: z 1 z 2 + iz 3 = 2 i (1 + i ) z 1 iz 2 + iz 3 = 2 + i (1 i ) z 1 + ( 1 + 2 i ) z 2 + (1 + 2 i ) z 3 = 3 + 2 i a) Row reduce the matrix to RREF using elementary row operations....
View
Full
Document
This note was uploaded on 01/18/2011 for the course MATH 136 taught by Professor All during the Winter '08 term at Waterloo.
 Winter '08
 All
 Math, Linear Algebra, Algebra

Click to edit the document details