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Question

Consider a system of linear equation:
x2y+3z=1
x3y+4z=1 and
2x+4y6z=k
The value of K for which the system has infinitely many solutions is

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Solution

[A:B]=⎢ ⎢ ⎢ ⎢12311341246K⎥ ⎥ ⎥ ⎥
R2R2R1,R3R3+2R1
⎢ ⎢ ⎢ ⎢12310112000K2⎥ ⎥ ⎥ ⎥
The system has infinite many solutions
rank(A)=rank(A:B)<n
k2=0
k=2

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