Docsity
Docsity

Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity


Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan


Guidelines and tips
Guidelines and tips

Math 308 H Exam II Autumn 2013, Exams of Linear Algebra

An exam for Math 308 H course taken in Autumn 2013 at the University of Washington. The exam consists of a cover sheet and 6 problems related to linear algebra. The exam instructions include an honor statement, time limit, and rules for calculator and notes usage. The problems require showing all work and justifying answers. The exam covers topics such as echelon form, column space, row space, null space, and basis for vector spaces.

Typology: Exams

2012/2013

Uploaded on 05/11/2023

unknown user
unknown user 🇺🇸

1 / 6

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
MATH 308 H
Exam II
Autumn 2013
Name Student ID #
HONOR STATEMENT
“I affirm that my work upholds the highest standards of honesty and academic integrity at the
University of Washington, and that I have neither given nor received any unauthorized assistance
on this exam.”
SIGNATURE:
1 10
2 4
3 6
4 8
5 12
6 10
Total 50
Your exam should consist of this cover sheet, followed by 6 problems. Check that you have
a complete exam.
Pace yourself. You have 50 minutes to complete the exam and there are 5 pages. Try not
to spend more than about 10 minutes on each page.
Unless otherwise indicated, show all your work and justify your answers.
Unless otherwise indicated, your answers should be exact values rather than decimal approx-
imations. (For example, π
4is an exact answer and is preferable to its decimal approximation
0.7854.)
Do not use scratch paper. Put all your work on the exam. If you run out of room, use the
back of the page and indicate to the reader you have done so.
You may use a scientific calculator and one 8.5×11-inch sheet of handwritten notes. All
other electronic devices (including graphing calculators) are forbidden.
The use of headphones or earbuds during the exam is not permitted.
There are multiple versions of the exam, you have signed an honor statement, and cheating
is a hassle for everyone involved. DO NOT CHEAT.
Turn your cell phone OFF and put it AWAY for the duration of the exam.
GOOD LUCK!
pf3
pf4
pf5

Partial preview of the text

Download Math 308 H Exam II Autumn 2013 and more Exams Linear Algebra in PDF only on Docsity!

MATH 308 H

Exam II Autumn 2013

Name Student ID #

HONOR STATEMENT

“I affirm that my work upholds the highest standards of honesty and academic integrity at the University of Washington, and that I have neither given nor received any unauthorized assistance on this exam.”

SIGNATURE:

Total 50

  • Your exam should consist of this cover sheet, followed by 6 problems. Check that you have a complete exam.
  • Pace yourself. You have 50 minutes to complete the exam and there are 5 pages. Try not to spend more than about 10 minutes on each page.
  • Unless otherwise indicated, show all your work and justify your answers.
  • Unless otherwise indicated, your answers should be exact values rather than decimal approx- imations. (For example, π 4 is an exact answer and is preferable to its decimal approximation 0.7854.)
  • Do not use scratch paper. Put all your work on the exam. If you run out of room, use the back of the page and indicate to the reader you have done so.
  • You may use a scientific calculator and one 8.5×11-inch sheet of handwritten notes. All other electronic devices (including graphing calculators) are forbidden.
  • The use of headphones or earbuds during the exam is not permitted.
  • There are multiple versions of the exam, you have signed an honor statement, and cheating is a hassle for everyone involved. DO NOT CHEAT.
  • Turn your cell phone OFF and put it AWAY for the duration of the exam.

GOOD LUCK!

  1. (10 points) Indicate whether the statement is true (T) or false (F). Circle your response. You are not required to show any work.

(a) If B is an echelon form of a matrix A, then the pivot columns of B form a basis for the column space of A. ANSWER: (circle one) T F

(b) The column space of a matrix A is equal to the row space of AT^. ANSWER: (circle one) T F

(c) The range of a linear transformation T must contain infinitely many elements. ANSWER: (circle one) T F

(d) If T : Rm^ → Rn^ is a linear transformation, then ker(T ) is a subspace of Rn. ANSWER: (circle one) T F

(e)

 (^) is in the null space of the matrix

ANSWER: (circle one) T F

  1. (8 points) Give an example of:

(a) a 3 × 3 matrix A such that row(A) = col(A)

(b) a singular 2 × 2 matrix with no zero entries

(c) a matrix A whose inverse is

[

]

(d) a linear transformation T such that T

[

]

and T (x) = Ax, where A

is a matrix with no zero entries

  1. (12 points) Let A =

(a) Compute rank(A) and nullity(A).

(b) Give a basis for the row space of A.

(c) Give a basis for the null space of A.