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MATH 1025 Study Guide - Midterm Guide: Linear Combination, Gaussian Elimination, Matrix MultiplicationExam


Department
Mathematics and Statistics
Course Code
MATH 1025
Professor
Asia Weiss
Study Guide
Midterm

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YORK UNIVERSITY
Faculty of Science
Department of Mathematics and Statistics
MATH 1025 3.00 – Section N
Test #2 March 01, 2019
Solutions
INSTRUCTIONS:
1. This is a closed book, closed notes test, duration – 50 minutes.
2. Calculators, Internet connected devices or other aids are NOT permitted.
3. There are 5 questions on pages 2 – 6. Answer the all questions.
4. Your work must justify your answers. Show your work on the space provided. Write your
solutions only on pages 2 – 6. Check the backs of the sheets for questions.
5. Do the easiest questions first, GOOD LUCK!
6. Remain seated until we collect all the test papers.
Copyright 2019 c
I. Raguimov

Only pages 1-2 are available for preview. Some parts have been intentionally blurred.

1. (8 + 4 pts) Given the system of linear equations
x1+ 2x23x3+x4=2
3x1x22x34x4= 1
2x1+ 3x25x3+x4=3.
(a) Find all solutions of the system using Gaussian elimination or Gauss-Jordan elimination.
ANSWER:
We have (it is not necessary that you indicate the EROs)
1 2 3 1 2
31241
2 3 5 1 3
R23R1
R32R1
1 2 3 1 2
07 7 77
01 1 11
(
1
7)R2
1 2 3 1 2
0 1 1 1 1
01 1 1 1
R12R2
R3+R2
1 0 110
0 1 1 1 1
0 0 0 0 0
Let x3=sand x4=tfor all real sand t.
Then we have the general solution
x1=s+t, x2=st1, x3=s, x4=t.
Or equivalent, using Gaussian elimination and back-substitution.
2
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