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Chapter 2 Section 2. Lemma 2.2.1 Let i=1 and j=2, then.

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Presentation on theme: "Chapter 2 Section 2. Lemma 2.2.1 Let i=1 and j=2, then."— Presentation transcript:

1 Chapter 2 Section 2

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

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

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

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

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

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

8 Lemma 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

13

14

15

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


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