# MATH 1025 Study Guide - Midterm Guide: Linear Combination, Elementary Matrix, Linear MapExam

by OC2540294

School

York UniversityDepartment

Mathematics and StatisticsCourse Code

MATH 1025Professor

AllStudy Guide

MidtermThis

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1!

York University

Department of Mathematics and Statistics

Faculty of Science

MATH 1021 Linear Algebra I

Final Examination

NAME:_____________________________________________________

(Family) (Given)

SIGNATURE:_______________________________________________

STUDENT NUMBER:________________________________________

Please indicate you section: Section A (Weiss) ☐

Section B (Poliakov) ☐

Instructions:

1. Duration 120 minutes.

2. NO CALCULATORS OR OTHER AIDS PERMITTED.

3. Show all your work.

4. All your answers must be justified.

5. Use back of the pages for any scrap work..

6. There are 9 questions. Total number of pages is 11.

Question

Points

Marks

1

12

2

10

3

12

4

12

5

12

6

10

7

10

8

10

9

12

Total

100

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!

2!

Question 1 [12 points]

Solve the following system of equations. Find a set of basic solutions and express the general

solution as a linear combination of these basic solutions.

023

063

0862

4321

4321

4321

=+−+−

=+−−

=+−−

xxxx

xxxx

xxxx

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

!

3!

Question 2 [10 points]

Given that

a b c

d e f

g h 1

=3

, find

4g4h4i

a b c

d−2a e −2b f −2c

using the property of determinants

in terms of elementary row operations.

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