If the system of equations $ \begin{aligned} & x+y+z=6 \ & x+2 y+3 z=10 \ & x+2 y+\lambda z=0 \end{aligned} $ has a unique solution, then $\lambda$ is not equal to

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Aicharya · Accepted Answer

Given system of equations is $ \begin{aligned} & x+y+z=6 \ & x+2 y+3 z=10 \ & x+2 y+\lambda z=0 \end{aligned} $ It has unique solution. $ \begin{aligned} & 	herefore\left|\begin{array}{lll} 1 & 1 & 1 \ 1 & 2 & 3 \ 1 & 2 & \lambda \end{array}ight| 
eq 0 \ & \Rightarrow \quad 1(2 \lambda-6)-1(\lambda-3)+1(2-2) 
eq 0 \ & \Rightarrow \quad 2 \lambda-6-\lambda+3 
eq 0 \Rightarrow \lambda-3 
eq 0 \Rightarrow \lambda 
eq 3 \end{aligned} $

If the system of equations $ \begin{aligned} & x+y+z=6 \\ & x+2 y+3 z=10 \\ & x+2 y+\lambda z=0…

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