Unformatted text preview: /'—‘. .r"a._ EXERCISES 3.4 43 17. We present a sequence of elementary row operations that lead to a row echelon form for
the augmented matrix of the given system. You may, however, use a different sequence of
operations, resulting in a different rowr echelon form. The solution of the system, however, must be the same.
1 1 —2 4 1 l ~—2
1 3 1 6 R2—1—R14R2 we 0 2 3
3 —1 2 7 Raﬁ—3R1+R3 0 —4 8
1 1 #2
—> 0 2 3 0014 2
—5) R3—12R2+R3 l1 1 1 *2 4
2 sadism —. 0 1 3/2 1
~1 Rg—DR3/14  o o 1 —1/14 We now convert this augmented matrix to an equivalent system of equations, :c+y—2z=4,
y+§z=1
2 I
z=_i.
14 When we substitute 2 = *1/14 into the second equation, we obtain + ——— => —1+3—El
3" 2 14" 3" 28‘28' When we substitute 3; = 31/28 and z = —1/14 into the ﬁrst equation, we get 31 1 31 1 11
m+——2(——)—4 => m4~§§—?_T. 18. We present a sequence of elementary row operations that lead to a row echelon form for the augmented matrix of the given system. You may, however, use a different sequence of _ operations, resulting in a different row echelon form. The solution of the system, however,
must be the same. '  4 1 —2 4 Rl—r—B,§+R, 1 2 —4 —3
2 3 1 s ———) 23 1 6 Rg—r—2R1+Rz
3 #1 2 7 3 —1 2 7 Raﬁ—3R14Rs
1 2 —4 —3 . 1 2 —4 —3
—¥ 0 1 9 12 R2 —> —R2 —* 0 1 9 ~12
0 L7 14 16 O —7 14 16 R3 —> 7R2 + R3
1 2 —4 —3 1 2 —4 #3
—1 0 1 —9 ~12 —) O 1 —9 —12
 0 0 —49 —68 3,; —> 413/49 0 D 1 68/49 We now convert this augmented matrix to an equivalent system of equations, w+2y—4z=—3, y—Qz=#12,
z—@
_49. When we substitute 2 = 68/49 into the second equation, we obtain 4. _:_ n. __ I. ___ _____ Lu”) :_ ......_A'.._.... "at. nnMn—Jn‘l. In“. I." it... 'l'lninmilunI‘IIanﬂnka nanlrdnm 11""th ramxﬂnnﬁm Iﬂ nnrf hr in HI“ 3!: £1!"le mhlhi'lﬂ‘l. ...
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 Fall '11
 Dr.Cornell
 Math

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