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Midterm

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


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

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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

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3!
Question 2 [10 points]
Given that
a b c
d e f
g h 1
=3
, find
using the property of determinants
in terms of elementary row operations.
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