System of equations :
Qx + y + z = Q-1 , x + Qy + z =Q-1 , x + y + Qz = Q-1

Has no solution if $Q>0$ , then what is the value of $Q$?

I want to solve this using matrices , so I used an augmented matrix for these matrices . I tried converting them into a reduced row echelon form matrix ,but even after a certain amount of operations I’m not able to fully arrive at a matrix where i can successfully apply the gauss Jordan elimination method

  • $\begingroup$ Is this $Q\cdot x$ or $Qx$ another variable? $\endgroup$ – Dr. Sonnhard Graubner Aug 1 at 17:18
  • $\begingroup$ Just Q .x , as In a linear question in x , y and z with Q as a constant . $\endgroup$ – H0RS3 Aug 1 at 17:32
  • $\begingroup$ Ah, $Q$ is supposed to be a parameter. $\endgroup$ – Dr. Sonnhard Graubner Aug 1 at 17:36

Using the Gauss algorithm we get $$x=\frac{Q-1}{Q+2}=y=z$$


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