Consider the system of linear equations x+y+z=5,x+2y+ ^2z=9,x+3y+ z= , where , R.

Question

Consider the system of linear equations $x+y+z=5,x+2y+{\lambda }^{2}z=9,x+3y+\lambda z=\mu $, where $\lambda ,\mu \in R$. Then, which of the following statement is NOT correct?

Accepted Answer

$\begin{gathered} |\begin{array}{ccc}1 \quad  1 \quad  1 \ 1 \quad  2 \quad  {\lambda }^{2} \ 1 \quad  3 \quad  \lambda \end{array}|=0 \ \Rightarrow 2{\lambda }^{2}-\lambda -1=0 \ \lambda =1,-\frac{1}{2} \ |\begin{array}{ccc}1 \quad  1 \quad  5 \ 2 \quad  {\lambda }^{2} \quad  9 \ 3 \quad  \lambda  \quad  \mu \end{array}|=0\Rightarrow \mu =13 \end{gathered}$

Infinite solution $\lambda =1\&\mu =13$

For unique ${sol}^{n}\lambda 
e 1$

For no ${sol}^{n}\lambda =1\&\mu 
e 13$

If $\lambda 
e 1$ and $\mu 
e 13$

Considering the case when $\lambda =-\frac{1}{2}$ and $\mu 
e 13$ this will generate no solution case

Solutions · 1