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## Chapter 2

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