math125-lecture 2.1 - Sec 2.1 Thursday, February 04, 2010...

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Sec 2.1 Thursday, February 04, 2010 11:03 PM Section2dot1 Page 1
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coefficient matrix: augmented matrix: -3 7 -5 5 8 3 4 -7 1 -3 7 -5 -4 5 8 3 8 4 -7 1 2 x 1 x 2 x 3 2.1.1 Thursday, February 04, 2010 10:55 PM Section2dot1 Page 2
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coefficient matrix: augmented matrix: -3 7 -5 5 8 3 4 -7 1 -3 7 -5 -4 5 8 3 8 4 -7 1 2 x 1 x 2 x 3 A matrix is in row echelon form (ref) if it has the following 4 properties: 1. the first non-zero entry in each row is a 1 (a leading 1) 1. Yes 1. No Not in ref 2.1.2 Thursday, February 04, 2010 10:55 PM Section2dot1 Page 3
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coefficient matrix: augmented matrix: -3 7 -5 5 8 3 4 -7 1 -3 7 -5 -4 5 8 3 8 4 -7 1 2 x 1 x 2 x 3 A matrix is in row echelon form (ref) if it has the following 4 properties: 1. the first non-zero entry in each row is a 1 (a leading 1) 2. each entry below a leading 1 is a 0 1. Yes 2. Yes 1. No Not in ref 2.1.3 Thursday, February 04, 2010 10:55 PM Section2dot1 Page 4
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coefficient matrix: augmented matrix: -3 7 -5 5 8 3 4 -7 1 -3 7 -5 -4 5 8 3 8 4 -7 1 2 x 1 x 2 x 3 A matrix is in row echelon form (ref) if it has the following 4 properties: 1. the first non-zero entry in each row is a 1 (a leading 1) 2. each entry below a leading 1 is a 0 3. as you move down the rows, the leading 1's moved to the right 4. any row of all 0's is always at the bottom (or just above a row of all 0's) 1. Yes 2. Yes 3. Yes 1. No Not in ref 2.1.4 Thursday, February 04, 2010 10:55 PM Section2dot1 Page 5
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coefficient matrix: augmented matrix: -3 7 -5 5 8 3 4 -7 1 -3 7 -5 -4 5 8 3 8 4 -7 1 2 x 1 x 2 x 3 A matrix is in row echelon form (ref) if it has the following 4 properties: 1. the first non-zero entry in each row is a 1 (a leading 1) 2. each entry below a leading 1 is a 0 3. as you move down the rows, the leading 1's moved to the right 4. any row of all 0's is always at the bottom (or just above a row of all 0's) 1. Yes 2. Yes 3. Yes 4. Yes - It is in ref 1. No Not in ref But the coefficient matrix is in ref 2.1.5 Thursday, February 04, 2010 10:55 PM Section2dot1 Page 6
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interchange two rows R i R j multiply a row by a non-zero number R' i = k R i , k ≠ 0 add a multiple of one row to another R' j = R j + k R i 2.1.6 Friday, February 05, 2010 9:25 AM Section2dot1 Page 7
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interchange two rows R i R j multiply a row by a non-zero number R' i = k R i , k ≠ 0 add a multiple of one row to another
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This note was uploaded on 06/07/2011 for the course MATH 125 taught by Professor Tom during the Fall '07 term at University of Illinois at Urbana–Champaign.

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math125-lecture 2.1 - Sec 2.1 Thursday, February 04, 2010...

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