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Midterm

# MAT223 2012 Spring Term Test 1

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School
University of Toronto St. George
Department
Mathematics
Course
MAT223H1
Professor
all
Semester
Fall

Description
University of Toronto Department of Mathematics MAT223H1S Linear Algebra I Midterm Exam I February 17, 2012 S. Morgan, P. Mondal, H. Petzka, S. Uppal, Y. Zong 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 va1ia2le3 4 ;x ;x ;x is represented by the following augmented matrix: 2 3 3 8 ▯18 1 35 4 1 2 ▯4 0 11 5 1 3 ▯7 1 10 [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. Solve for X: [A(I + AB )] X = C where 0 1 0 1 0 1 1 0 0 0 0 0 3 6 A [email protected] 0 1 0A ;B [email protected] ▯2 0 ▯2 A ;C [email protected] 2 1 A ; 3 ▯2 9 2 0 0 ▯3 0
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