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Midterm

MATH 1025 Study Guide - Midterm Guide: Polynomial, Elementary Matrix, 32XExam


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

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York University
Faculty of Arts, Faculty of Science
Math 1025
Class Test 1
SOLUTIONS
Instructions:
1. Time allowed: 50 minutes
2. There are 5 questions on 5 pages.
3. Answer all questions.
4. Your work must justify the answer you give.
5. No calculators or other aids permitted.
Question Points Marks
1 13
2 7
3 7
4 7
5 6
Total 40

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MATH 1025 Test 1
Page 1
January 24, 2005
1. (a) (8 points) Find all solutions to
x1+ 3x22x3+ 5x4= 4
2x1+ 6x23x3+ 12x4= 9
3x1+ 9x27x3+ 13x4= 11 .
Answer: Reduce the augmented coefficient matrix.
1 3 2 5 4
2 6 3 12 9
3 9 7 13 11
1 3 2 5 4
0 0 1 2 1
0 0 121
1 3 2 5 4
0 0 1 2 1
0 0 0 0 0
13096
00121
00000
From which
x1= 6 9t3s
x2=s
x3= 1 2t
x4=t .
(b) (2 points) Is there a solution with x2= 1 and x4= 0? Find one or explain why not.
Answer: Yes. Set s= 1 and t= 0 to get x1= 3, x2= 1, x3= 1, x4= 0.
(c) (3 points) Is there a solution with x3= 0 and x4= 1? Find one or explain why not.
Answer: No. To obtain x4= 1 we need t= 1. To obtain x3= 0 we need t=1
2.
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