# Chapter 2

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## Chapter 2

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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 ET is also an elementary matrix and

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

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

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

16. Interchanging two rows (or columns) of a matrix changes the sign of the determinant. • 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. • Adding a multiple of one row (or column) to another does not change the value of the determinant

17. Interchanging two rows (or columns) of a matrix changes the sign of the determinant. • 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. • Adding a multiple of one row (or column) to another does not change the value of the determinant

18. Interchanging two rows (or columns) of a matrix changes the sign of the determinant. • 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. • Adding a multiple of one row (or column) to another does not change the value of the determinant

19. Interchanging two rows (or columns) of a matrix changes the sign of the determinant. • 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. • Adding a multiple of one row (or column) to another does not change the value of the determinant

20. Interchanging two rows (or columns) of a matrix changes the sign of the determinant. • 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. • Adding a multiple of one row (or column) to another does not change the value of the determinant

21. Interchanging two rows (or columns) of a matrix changes the sign of the determinant. • 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. • Adding a multiple of one row (or column) to another does not change the value of the determinant