Class Notes (923,248)
CA (543,180)
UTSC (33,026)
Mathematics (1,168)
MATA23H3 (77)
Lecture

Detereminants

7 Pages
81 Views

Department
Mathematics
Course Code
MATA23H3
Professor
Sophie Chrysostomou

This preview shows pages 1-2. Sign up to view the full 7 pages of the document.
Determinants
Areas,Volumesand Cross Products
Definition:(i)Thedeterminantof1×1matrixisits sole entry.
(ii)Thedeterminantofa2×2matrixisgiven by
det(A)=
a1a2
b1b2
=a1b2b1a2,whereA=a1a2
b1b2
(iii)Thedeterminantofa3×3matrixisgiven by
det(A)=
a1a2a3
b1b2b3
c1c2c3
=a1
b2b3
c2c3
a2
b1b3
c1c3
+a3
b1b2
c1c2
Definition:Ifa=[a1,a2,a3],b=[b1,b2,b3]R3thecross productofaand bisgiven
by
a×b="
a2a3
b2b3
,
a1a3
b1b3
,
a1a2
b1b2#=i
a2a3
b2b3
j
a1a3
b1b3
+k
a1a2
b1b2
Note:a×bisperpendicular tobothaand b.
1c
2011 bySophieChrysostomou
www.notesolution.com
Theorem:(i)Ifaparallelogramisdetermined bytwononzerovectors,a=[a1,a2]and
b=[b1,b2] inR2,thenitsareaisgiven by
Area=|a1b2a2b1|=
deta1a2
b1b2
=
a1a2
b1b2
(ii)Ifaparallelogramisdetermined bytwononzerovectors,a=[a1,a2,a3]and b=[b1,b2,b3]
inR3,thenitsareaisgiven byka×bk.
(iii)Ifaparallelepipedisdetermined bythree nonzerovectorsa=[a1,a2,a3], b=[b1,b2,b3]
and c=[c1,c2,c3] inR3,thenthevolumeoftheboxisgiven by
Volume=|a·(b×c)|
2c
2011 bySophieChrysostomou
www.notesolution.com

Loved by over 2.2 million students

Over 90% improved by at least one letter grade.

Leah — University of Toronto

OneClass has been such a huge help in my studies at UofT especially since I am a transfer student. OneClass is the study buddy I never had before and definitely gives me the extra push to get from a B to an A!

Leah — University of Toronto
Saarim — University of Michigan

Balancing social life With academics can be difficult, that is why I'm so glad that OneClass is out there where I can find the top notes for all of my classes. Now I can be the all-star student I want to be.

Saarim — University of Michigan
Jenna — University of Wisconsin

As a college student living on a college budget, I love how easy it is to earn gift cards just by submitting my notes.

Jenna — University of Wisconsin
Anne — University of California

OneClass has allowed me to catch up with my most difficult course! #lifesaver

Anne — University of California
Description
Determinants Areas, Volumes and Cross Products Denition: (i) The determinant of 1 1 matrix is its sole entry. (ii)The determinant of a 2 2 matrix is given by a1 a2 a1 a2 det(A) = = a 1 2 b a 1 2 where A = b1 b2 b1 b2 (iii) The determinant of a 3 3 matrix is given by a1 a 2 a 3 det(A) = b1 b2 b 3 = a 1 b2 b3 a 2 b1 b3 + a 3 b1 b2 c2 c3 c1 c3 c1 c2 c1 c2 c 3 Denition: If a = [a ,a ,1 ],2 = 3b ,b ,b ] 1 R 2he 3ross product of a and b is given by # a b = a2 a3 , a 1 a 3 , a 1 a 2 = i a2 a 3 j a1 a 3 + k a 1 a2 b2 b3 b1 b 3 b1 b 2 b2 b3 b1 b3 b 1 b2 Note: a b is perpendicular to both a and b. 1 2011 by Sophie Chrysostomou www.notesolution.com
More Less
Unlock Document


Only pages 1-2 are available for preview. Some parts have been intentionally blurred.

Unlock Document
You're Reading a Preview

Unlock to view full version

Unlock Document

Log In


OR

Don't have an account?

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


OR

By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.


Submit