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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