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#### Please provide solution for RD Sharma class 12 chapter 7 Solution of Simultaneous Linear  Exercise Fill in the blank  Question 2 Maths Textbook solution.

Answer $\rightarrow \lambda =3$

Given $\rightarrow$ We have, the given system of equations $x+y+z=6, x+2 y+3 z=10, x+2 y+\lambda z=12$ is inconsistent.

To find $\rightarrow$ The value of $\lambda$

Hint $\rightarrow$ For inconsistent, determinant of the given system of equation will be zero i.e.$D=0$

Solution $\rightarrow$  We know that

\begin{aligned} &x+y+z=6 \\ &x+2 y+3 z=10 \\ &x+2 y+\lambda z=12 \end{aligned}

Here, we know that for inconsistent then $D=0$

$\Rightarrow\left|\begin{array}{lll} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 2 & \lambda \end{array}\right|=0$

Expanding along row $1$ we get

\begin{aligned} &\Rightarrow 1(2 \lambda-6)-1(\lambda-3)+1(2-2)=0\\ &\Rightarrow 2 \lambda-6-\lambda+3=0\\ &\Rightarrow \lambda-3=0\\ &\Rightarrow \lambda=3 \text { is required solution. } \end{aligned}