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# HW3 - 9.8(a The system is first expressed as an augmented...

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9.8 (a) The system is first expressed as an augmented matrix: 5 . 21 5 1 1 5 . 61 2 6 3 27 1 2 10 Forward elimination: a 21 is eliminated by multiplying row 1 by –3/10 and subtracting the result from row 2. a 31 is eliminated by multiplying row 1 by 1/10 and subtracting the result from row 3. 2 . 24 1 . 5 8 . 0 0 4 . 53 7 . 1 4 . 5 0 27 1 2 10 a 32 is eliminated by multiplying row 2 by 0.8/(–5.4) and subtracting the result from row 3. 1111 . 32 351852 . 5 0 0 4 . 53 7 . 1 4 . 5 0 27 1 2 10 Back substitution: 6 351852 . 5 1111 . 32 3 = = x 8 4 . 5 ) 6 ( 7 . 1 4 . 53 2 = = x 5 . 0 10 ) 8 ( 2 ) 6 )( 1 ( 27 1 = = x (b) Check: 5 . 21 ) 6 ( 5 8 5 . 0 5 . 61 ) 6 ( 2 ) 8 ( 6 ) 5 . 0 ( 3 27 ) 6 ( ) 8 ( 2 ) 5 . 0 ( 10 = + + = + = + 10.2 (a) The coefficient a 21 is eliminated by multiplying row 1 by f 21 = –3/10 = –0.3 and subtracting the result from row 2. a 31 is eliminated by multiplying row 1 by f 31 = 1/10 = 0.1 and subtracting the result from row 3. The factors f 21 and f 31 can be stored in a 21 and a 31 . 1 . 5 8 . 0 1 . 0 7 . 1 4 . 5 3 . 0 1 2 10 a 32 is eliminated by multiplying row 2 by f 32 = 0.8/(–5.4) = –0.14815 and subtracting the result from row 3. The factor f 32 can be stored in a 32 .

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