Docsity
Log inSign up
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
Sell on Docsity
Sell on Docsity
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search Store documents

The best documents sold by students who completed their studies

Search through all study resources
Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

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

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

University Rankings

Discover the best universities in your country according to Docsity users

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

From our blog

Exams and Study
Go to the blog

Inverse of a Matrix - Lecture Slides | MATH 101, Study notes of Algebra

Harford Community CollegeAlgebra

Material Type: Notes; Class: College Algebra (GM); Subject: Mathematics; University: Harford Community College; Term: Spring 2009;

Typology: Study notes

Pre 2010

Uploaded on 08/18/2009

koofers-user-p6u
koofers-user-p6u 🇺🇸

10 documents

1 / 6

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
4/20/2009
1
Inverse of a Matrix
MATH 101
College Algebra
S. Rook
2
Overview
• Section 7.3 in the textbook:
– Finding the Inverse of a Matrix
– Singular Matrices
– Solving Systems of Equations Using the
Inverse of a Matrix
Finding the Inverse of a Matrix
pf3
pf4
pf5

Partial preview of the text

Download Inverse of a Matrix - Lecture Slides | MATH 101 and more Study notes Algebra in PDF only on Docsity!

Inverse of a Matrix

MATH 101

College Algebra

S. Rook

2

Overview

  • Section 7.3 in the textbook:
    • Finding the Inverse of a Matrix
    • Singular Matrices
    • Solving Systems of Equations Using the

Inverse of a Matrix

Finding the Inverse of a Matrix

4

Multiplicative Identity and Inverse

for Real Numbers

  • Recall the concepts of the multiplicative

identity and the multiplicative inverse for

real numbers:

  • Multiplicative identity: 1
    • c multiplied by 1 remains c
  • Multiplicative inverse: 1 /c
    • c multiplied by^1 /c (its reciprocal) is 1
  • As we will see, these same properties

have parallels for matrices

5

Identity Matrix

  • Identity Matrix: a square matrix whose

elements along its main diagonal are 1 and

other elements are 0

  • Recall a square matrix has dimensions of n x n
  • The identity matrix is the matrix equivalent of

the real number 1

  • Often abbreviated as I n where n

represents an n x n square matrix

  • I 2 is pictured to the right

6

Multiplicative Identity and Inverse

for Matrices

  • An m x n matrix A multiplied by

the n x n identity matrix will retain the same values

A · I n = A

  • An m x n matrix A multiplied by its

m x n multiplicative inverse A -

will yield the n x n identity matrix

  • Often just called the inverse of a matrix

A · A -1^ = A -1^ · A = I n

^ =

Singular Matrices

11

Singular Matrices

  • Singular Matrix: a matrix that DOES

NOT have an inverse

  • Nonsingular Matrix: a matrix that DOES

have an inverse

  • A matrix is singular if a row of zeros

appears in A while transforming A to A

12

Singular Matrices (Example)

Ex 3: Show that the matrix is singular:

a)

b)

Solving Systems of Equations

Using the Inverse of a Matrix

14

Solving Systems of Equations

Using the Inverse of a Matrix

  • Recall that we can decompose a system

of equations into a coefficient matrix , a

variable matrix , and a constant matrix

  • Let A be the coefficient matrix, X be the

variable matrix, and B be the constant

matrix

  • Then we can write the system as AX = B

AX = B → A

  • · AX = A - · B → X = A - · B
  • Why can’t we say B · A-1?

15

Solving Systems of Equations Using

the Inverse of a Matrix (Example)

Ex 4: Solve the system of equations by using the

inverse of the coefficient matrix:

a) b)

x y

x y

y z

x y z

x z