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Question

Show that the equations x+y+z=6,x+2y+3z=14,x+4y+7z=30 are consistent and solve them.

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Solution

x+y+z=6,x+2y+3z=14
x+4y+7z=30
AX=D
A=111123147 X=xyz
Consider Aqument matrix
AD=11161231414730
R2:R2R1;R3:R3R1
AD=1116012803624
R3:R33R2
AD=111601280000
Rank of AD=2 &
Rank of A=2
It is consistent
x+y+z=6;y+z=8
x+8=6 y=k
x=2 z=8k
The system is consistent
but has infinite many solutions
x=2,y=k,z=8k
KR is solution set.

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