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Midterm

MAT223 2011 Fall Term Test 1

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Department
Mathematics
Course
MAT223H1
Professor
All Professors
Semester
Fall

Description
University of Toronto Department of Mathematics MAT223H1F Linear Algebra I Midterm Exam I October 20, 2011 C. Anghel, S. Arkhipov, S. Shahroki-Tehrani, S. Uppal Duration: 1 hour 30 minutes Last Name: Given Name: Student Number: Tutorial Group: No calculators or other aids are allowed. FOR MARKER USE ONLY Question Mark 1 /10 2 /10 3 /10 4 /10 5 /10 6 /5 TOTAL /55 1 of 10 1. A system of linear equations in the var1ab2e3 x4;x ;x ;x is represented by the following augmented matrix: 2 3 1 0 1 0 2 4 2 1 0 1 3 5 3 1 1 1 5 [6] (a) Find the reduced row-echelon form of the augmented matrix. [1] (b) How many parameters are required to solve the system? [3] (d) Find the general solution to the system. Express your answer in parametric form. 2 of 10 EXTRA PAGE FOR QUESTION 1 - do not remove. 3 of 10 [10] 2. Consider the system of linear equations ax 1 3x =21 4x 1 bx =2▯2 (a) Find real numbers a and b such that the linear system has an in▯nit
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