Midterm 1 Review Sheet
Math 19652, Spring 2017
April 14, 2017
Contents
1
Main Concepts
2
2
Main Theorems
2
3
Standard Problem Types
2
4
Conceptual Problems
3
1 Main Concepts
2
Suggestions for Review Order:
1. Quizzes (review the solutions in sample quiz
REVIEW SHEET FOR FINAL: ADVANCED
MATH 196, SECTION 59 (VIPUL NAIK)
To maximize eciency, please bring a copy (print or readable electronic) of this review sheet
to the Saturday/Sunday review sesssion.
Please come to the session only if you know the meaning
TAKEHOME CLASS QUIZ: DUE MONDAY APRIL 15: MATRIX COMPUTATIONS
MATH 196, SECTION 59 (VIPUL NAIK)
Your name (print clearly in capital letters):
PLEASE DO NOT DISCUSS ANY QUESTIONS EXCEPT THE STARRED OR DOUBLESTARRED QUESTIONS.
Suppose f is a function on th
TAKEHOME CLASS QUIZ: DUE FRIDAY APRIL 12: LINEAR SYSTEMS
MATH 196, SECTION 59 (VIPUL NAIK)
Your name (print clearly in capital letters):
PLEASE DO NOT DISCUSS ANY QUESTIONS EXCEPT THE STARRED OR DOUBLESTARRED QUESTIONS.
(1) (*) Rashid and Riena are tryin
Math 196, Section 55
Instructor: Chris Skalit
First Hour Exam
You have 50 minutes to complete the exam. The use of calculators, cellphones, notebooks,
etc. is strictly prohibited. Partial credit will be awarded for answers that are either incomplete or sl
Math 196, Section 55
Instructor: Chris Skalit
Quiz 1
Name:
1. Find all solution(s) to the following systems of linear equations:
(a) (4 points)
4x 4y
= 12
2x + y
=5
3x
+ z = 7
4 4 0 12
1 0 5 .
Solution: We represent our system via the augmented matrix, A
Math 196, Section 55
Instructor: Chris Skalit
Least Squares Practice
Name:
1. Consider the points (0, 1), (1, 1), (2, 3), (3, 4) in the plane. Find the best t line of the
form, y = mx + b, for these points using least squares.
Solution: We are attempting
Math 196, Section 55
Instructor: Chris Skalit
Quiz 2
Name:
1. Suppose that T : R2 R3 is a linear transformation such that
1
0
0
1
T
= 2
T
= 0
0
1
3
4
(a) (2 points) What is the matrix, A, for T ?
Solution: Remember that A is merely the 3 2 matrix whose
Math 196, Section 55
Instructor: Chris Skalit
Quiz 6
Name:
1. (5 points) Consider the subspace, V , of R4 that is spanned by the vectors,
1
0
0
1
0
0
v1 =
v2 =
v3 =
1
1
0
1
1
4
Use GramSchmidt to nd an orthonormal basis for V .
Solution: By GramSchmi
Math 196, Section 55
Instructor: Chris Skalit
Quiz 5
Name:
1. Consider the vector space, V = P2 , the space of polynomials of degree at most 2.
Consider the elements
f 1 = x2
f2 = x
f3 = 1
g 1 = x2
g2 = x + 3
g3 = x + 2
You may take for granted that A = (
REVIEW SHEET FOR FINAL: BASIC
MATH 196, SECTION 59 (VIPUL NAIK)
The document does not include material that was part of the midterm 1 and midterm 2 review sessions.
Please review these on your own time.
You are expected to review this on your own time. We
REVIEW SHEET FOR MIDTERM 1: BASIC
MATH 196, SECTION 59 (VIPUL NAIK)
We will not be going over this sheet, but rather, well be going over the advanced review sheet in the
session. Please review this sheet on your own time.
The summaries here are identical
REVIEW SHEET FOR MIDTERM 1: ADVANCED
MATH 196, SECTION 59 (VIPUL NAIK)
Please bring a copy (print or readable electronic) of this sheet to the review session.
There is also a basic review sheet that contains executive summaries of the lecture notes. You s
Short Stories
Exam Review
Short story exam: Sampler
Although this specific question isnt on the test, it is
typical of the multiple choice questions youll see:
(MARIGOLDS): Which of the following is NOT a reason
that annoying Miss Lottie is usually fun?
A
TAKEHOME CLASS QUIZ: DUE WEDNESDAY APRIL 10: LINEAR FUNCTIONS
AND EQUATIONSOLVING (PART 2)
MATH 196, SECTION 59 (VIPUL NAIK)
Your name (print clearly in capital letters):
PLEASE DO NOT DISCUSS ANY QUESTIONS EXCEPT THE STARRED OR DOUBLESTARRED QUESTIONS.
TAKEHOME CLASS QUIZ: DUE WEDNESDAY MAY 15: IMAGE AND KERNEL
MATH 196, SECTION 59 (VIPUL NAIK)
Your name (print clearly in capital letters):
PLEASE FEEL FREE TO DISCUSS ALL QUESTIONS.
(1) Suppose g : A B and f : B C are functions. The composite f g is a f
TAKEHOME CLASS QUIZ: DUE MONDAY JUNE 3: SUBSPACE, BASIS,
DIMENSION, COORDINATES, AND ABSTRACT SPACES
MATH 196, SECTION 59 (VIPUL NAIK)
Your name (print clearly in capital letters):
PLEASE FEEL FREE TO DISCUSS ALL QUESTIONS.
Keep in mind the following fac
TAKEHOME CLASS QUIZ: DUE FRIDAY MAY 3: MATRIX MULTIPLICATION
AND INVERSION
MATH 196, SECTION 59 (VIPUL NAIK)
Your name (print clearly in capital letters):
PLEASE FEEL FREE TO DISCUSS ALL QUESTIONS.
(1) How many arithmetic operations are needed for naive
TAKEHOME CLASS QUIZ: DUE FRIDAY APRIL 26: GEOMETRY OF LINEAR
TRANSFORMATIONS
MATH 196, SECTION 59 (VIPUL NAIK)
Your name (print clearly in capital letters):
PLEASE FEEL FREE TO DISCUSS ALL QUESTIONS.
For the questions here, please use the following termi
TAKEHOME CLASS QUIZ: DUE FRIDAY APRIL 19: LINEAR SYSTEMS: RANK
AND DIMENSION CONSIDERATIONS
MATH 196, SECTION 59 (VIPUL NAIK)
Your name (print clearly in capital letters):
PLEASE DO NOT DISCUSS ANY QUESTIONS EXCEPT THE STARRED OR DOUBLESTARRED QUESTIONS.
TAKEHOME CLASS QUIZ: DUE FRIDAY MAY 10: LINEAR TRANSFORMATIONS
(MISCELLANEA)
MATH 196, SECTION 59 (VIPUL NAIK)
Your name (print clearly in capital letters):
PLEASE FEEL FREE TO DISCUSS ALL QUESTIONS.
Let n be a natural number greater than 1. Suppose f :
TAKEHOME CLASS QUIZ: DUE FRIDAY JUNE 7 (OR LATER): SIMILARITY OF
LINEAR TRANSFORMATIONS
MATH 196, SECTION 59 (VIPUL NAIK)
Your name (print clearly in capital letters):
PLEASE FEEL FREE TO DISCUSS ALL QUESTIONS.
Note: The ocial deadline is Friday June 7.
TAKEHOME CLASS QUIZ: DUE FRIDAY APRIL 5: LINEAR FUNCTIONS AND
EQUATIONSOLVING (PART 1)
MATH 196, SECTION 59 (VIPUL NAIK)
Your name (print clearly in capital letters):
PLEASE DO NOT DISCUSS ANY QUESTIONS EXCEPT THE STARRED OR DOUBLESTARRED QUESTIONS.
(1)
Math 196, Section 55
Instructor: Chris Skalit
Quiz 4
Name:
1. (4 points) Let V be the linear space of 2 2 matrices, A, which satisfy the equation,
1
2
A
0
0
=
Find a basis for V .
ab
cd
Solution: Let A =
V . We therefore have
a 2b
c 2d
ab
cd
=
1
2
=
0
0
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