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Question

 1 x1 +0 x2 -4 x3 -6 x4  = 17

 0 x1 +4 x2 -2 x3 -2 x4  = -18

-4 x1 -2 x2 +21 x3 +35 x4  = -77

-6 x1 -2 x2 +35 x3 +78 x4  = -154

Answer 1

(I) 1*x1 +0*x2 -4*x3 -6*x4  = 17

(II) 0*x1 +4*x2 -2*x3 -2*x4  = -18

(III) -4*x1 -2*x2 +21*x3 +35*x4  = -77

(IV) -6*x1 -2*x2 +35*x3 +78*x4  = -154 

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	x1	x2	x3	x4
(I)	1	0	-4	-6	17
(II)	0	4	-2	-2	-18
(III)	-4	-2	21	35	-77
(IV)	-6	-2	35	78	-154

(II)	0	4	-2	-2	-18
(I)*4+(III)	0	-2	5	11	-9	(III)'
(I)*6+(IV)	0	-2	11	42	-52	(IV)'

(III)'-(IV)'	0	0	-6	-31	43	(III)''
(II)*0,5+(IV)'	0	0	10	41	-61	(IV)''

(III)''*10+(IV)''*6

0

0

0

-64

64

(IV)'''

aus (IV)''': -64*x4=64 => x4=-1

x4 in (IV)'': 10x3+41*(-1)=-61 => 10x3-41=-61 => x3=-2

x3, x4 in (IV)': -2x2+11*(-2)+42*(-1)=-52 => -2x2-64=-52 => x2=-6

x2, x3, x3 in (I): x1-4*(-2)-6*(-1)=17 => x1+14=17 => x1=3