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

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Chapter 2 Section 2

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

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

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

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

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

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

Lemma 2.2.1 Notice where

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

Multiplying Row 3 by 4 and calculating the determinant,

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

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

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

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

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

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

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

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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