Download presentation

Presentation is loading. Please wait.

Published byHaleigh Deaton Modified over 2 years ago

1
Chapter 2 Section 2

2
Lemma 2.2.1 Let i=1 and j=2, then

3
Lemma 2.2.1 Let i=1 and j=2, then

4
Lemma 2.2.1 Let i=1 and j=2, then

5
Lemma 2.2.1 Let i=1 and j=2, then

6
Lemma 2.2.1 Let i=1 and j=2, then

7
Lemma 2.2.1 Let i=1 and j=2, then

8
Lemma 2.2.1 Notice where

9
Switching Row 2 and Row 3, and calculating the determinant,

10
Multiplying Row 3 by 4 and calculating the determinant,

11
If E is an elementary matrix, then where If E is of type I If E is of type II If E is of type III

12
Similar results hold for column operations. Indeed, if E is an elementary matrix, then E T is also an elementary matrix and

16
I.Interchanging two rows (or columns) of a matrix changes the sign of the determinant. II.Multiplying a single row (or column) of a matrix by a scalar has the effect of multiplying the value of the determinant by that scalar. III.Adding a multiple of one row (or column) to another does not change the value of the determinant

17
I.Interchanging two rows (or columns) of a matrix changes the sign of the determinant. II.Multiplying a single row (or column) of a matrix by a scalar has the effect of multiplying the value of the determinant by that scalar. III.Adding a multiple of one row (or column) to another does not change the value of the determinant

18
I.Interchanging two rows (or columns) of a matrix changes the sign of the determinant. II.Multiplying a single row (or column) of a matrix by a scalar has the effect of multiplying the value of the determinant by that scalar. III.Adding a multiple of one row (or column) to another does not change the value of the determinant

19
I.Interchanging two rows (or columns) of a matrix changes the sign of the determinant. II.Multiplying a single row (or column) of a matrix by a scalar has the effect of multiplying the value of the determinant by that scalar. III.Adding a multiple of one row (or column) to another does not change the value of the determinant

20
I.Interchanging two rows (or columns) of a matrix changes the sign of the determinant. II.Multiplying a single row (or column) of a matrix by a scalar has the effect of multiplying the value of the determinant by that scalar. III.Adding a multiple of one row (or column) to another does not change the value of the determinant

21
I.Interchanging two rows (or columns) of a matrix changes the sign of the determinant. II.Multiplying a single row (or column) of a matrix by a scalar has the effect of multiplying the value of the determinant by that scalar. III.Adding a multiple of one row (or column) to another does not change the value of the determinant

Similar presentations

OK

AIM: How do we perform basic matrix operations? DO NOW: Describe the steps for solving a system of Inequalities How do you know which region is shaded?

AIM: How do we perform basic matrix operations? DO NOW: Describe the steps for solving a system of Inequalities How do you know which region is shaded?

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google