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Applied Finite Mathematics HW Solutions 42

Applied Finite Mathematics HW Solutions 42 - 40 EXERCISES...

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Unformatted text preview: 40 EXERCISES 3.4 10. 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 he the same. 2 1 {*3 4 R1 —} .34; 1 —1 U 1 —1 0 6 R2 ~—r R1 we 2 1 —3 5 1 —fi 6 4) Rz—r—2R1‘i'R/3 14 5 1 —s 14 stoneware 1—1 0 6 1 —1 o s __, o 3 H3 “8 __, 0 3 F3 —8 Biz—’R/z/3 0 6 ~e ~16 Rah—232+Rs o o o o 1 H1 0 —‘ 0 1 —1 0 0 0 6 43/3) 0. We nowr convert this augmented matrix to an equivalent system of equations, CC _ y = 6a _ z _ _§ 3'! — 3- _ When We solve the second of these for y in terms of 2:, we obtain y = z — 8/3. We now substitute this into the first equation, 8 ' ‘ s 10 x—(z—§)-—6 => $#6+z—§—z+-§-. Thus, there is an infinity of solutions for the system - $=z+_~1§0-, y=z—%, z arbitrary. 11. 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. 1 1 —1 0 - 1 1 "-1 U 2 1 —1 0 resonates; —-+ 0 —1 1 0 R2'—>—R2 3 —4 2 0 R3 —> —3R1 + R3 0 --7 5 0 _ 1 1 —1 0 1 1 -1 0 —v-+ U 1 *1 0 n'"" 0 1 _1 0 0' _7 5 0' R3 —)7R/3+R3 0 U -2 0 R3 ~—!- —-R3/2 11—1 —v-+ 01-—-1 001 0 0 0 We now convert this augmented matrix to an equivalent system of equations, swig—4:0, y_z=03 z=0. These require that a: = y = z = 0. 'I'LL. _...4.._:..I‘I...... I...“ Manna :. -mmA--.“ ...:n. Ann—L.“ I..." t... 0.. I 701:“th a“. “Mani“. Mpg-Inn “unim- rmmdmfim in my: - in fil" Eu etch-flu Iu'nhihilfifl ...
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