Unformatted text preview: so ' ' _ EXERCISES 3.5 23. We presenta sequence of elementary row operations that lead to the reduced row echelon
form for the augmented .matrix of the given system. You might use a different sequence of operations. but since the reduced row echelon form is unique, you mustarrive at the same
augmented matrix. 1 1 1 1 5 1 1 1 1 *5
2 “3 1 “2 13 R2 + “2.31 I R2 _’ 0 5 3 4 23 R2 —¥ Re,
3 4 1 1 "6 R3—+—3R1+Rg U 1 2 ...2 9 R‘s—*Rz
1 1 0 2 “6 R4 + H31 *1" R4 0 0 1 1 1
1 1 1 1 “5 R1 + “R2 + R1 1 U “3 3 "14
_’ 0 1 2 —2 9 _’ 0 1 2 ...2 9
0 —5 3 —4 23 R3 —! 5R2 + R3 0 0 13 14_ 63 R3 + R4
0 0 1 1 r—l . 0 0 1 1 1 R4 + 3.3
1 0 3 3 14 R; '+ 33.3 + R1 1 0 0 5 17
_’ 0' 1 2 “2 9 R2 + “233 4 R2 _1. 0 1 0 —4 11
0 0 1 1 1  0 U 1 1 —1
0 0 13 H14 68 R4 + 1333 +34 0 0 0 “2'? 81 R4 —! —R4/27
l 0 0 5 —17. R1 +—6R4+R1 1 0 0 0 1
_1. 0 1 0 4 11 R2 + 434 + R2 0 1 U 0 1
U 0 1 l 1 R3 + —R4 + R3 0 0 1 U 2
0 0 0 1 “3 0 0 0 1 “3 The solution of the system is m = 1, y = —1, z z 2, w = M3. 24. We present a sequence of elementary row operations that lead to the reduced row echelon
‘ form for the augmented matrix of the given system. You might use a diﬂ'erent sequence of
operations, but since the reduced row echelon form is unique, you must arrive at the same ' augmented matrix. 2 —1 4‘ 1 —13 121—1123 1 —31 0 —«9
1 1 —2 3 11 1 1 H2 3 11 R2—+—Rl+R2
1 43 1 0 49 113.4131 _’ 2 —1 4 1 —13 R34~2R1 +133
0 4 2' —1 1 0 4 2 —1 1
1 43 1 0 —9 1 —3 1 0 —9
_’ 0 4 —3 3 20 _’ 0 4 —3 3 20 122—1133
0 5 2 1 5 Re—+~R4+R3 o 1 0 2 4 Its—+132
0. 4 2 —1 1 0 4 2 —1 1
1 —3 1 o 9 Elemental 1 0 1 6 3
_’ 0 1 0. 2 4 _’ _, 0 1 o 2 4
0 4 _3 3 20 R3—+4R2+R3 0 0 —3 5 4 3342134+Ra
0 4 2 —1 1 R44~4R2+R4 0 0 2 —9 ~15
1 0 1 6 3 R1H~R3+R1 10 0 29 29
_’ 0 1 0 2 4 ' _’ 0 1 0 2 4
001—23—26 001—23—46
0 0 2 —9 —15 R4—+—2R3+R«1 0 U 0 37 37 R4—4R4/37 Tm" “14.4.11 1...... 1...“... MA..MA :n "mum. .1... mm. nn‘ODri'nIui 1....r I.“ nw I hamsh“ n1! “want“. “rumbaCm trunks. fame1:". in rm rf m ;n H." :c «axnu nmh‘kiiar‘ ...
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 Fall '11
 Dr.Cornell
 Math

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