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

by OC2218391

School

York UniversityDepartment

Mathematics and StatisticsCourse Code

MATH 1025Professor

Asia WeissStudy Guide

MidtermThis

**preview**shows pages 1-2. to view the full**7 pages of the document.**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+ 2x2−3x3+x4=−2

3x1−x2−2x3−4x4= 1

2x1+ 3x2−5x3+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

3−1−2−41

2 3 −5 1 −3

R2−3R1

−−−−−→ R3−2R1

−−−−−→

1 2 −3 1 −2

0−7 7 −77

0−1 1 −11

(−

1

7)R2

−−−−−→

1 2 −3 1 −2

0 1 −1 1 −1

0−1 1 −1 1

R1−2R2

−−−−−→ R3+R2

−−−−→

1 0 −1−10

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=s−t−1, x3=s, x4=t.

Or equivalent, using Gaussian elimination and back-substitution.

2

###### You're Reading a Preview

Unlock to view full version