Consider the system of linear equations

x+ | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

$\begin{aligned} & \left|\begin{array}{ccc}1 & 1 & 1 \ 1 & 2 & \lambda^2 \ 1 & 3 & \lambda\end{array}ight|=0 \ &

Vedclass · Accepted Answer

System has unique solution if $\lambda 
eq 1$ and $\mu 
eq 13$

Vedclass · Answer

$\begin{aligned} & \left|\begin{array}{ccc}1 & 1 & 1 \ 1 & 2 & \lambda^2 \ 1 & 3 & \lambda\end{array}ight|=0 \ & \Rightarrow 2 \lambda^2-\lambda-1=0 \ & \lambda=1,-\frac{1}{2} \ & \left|\begin{array}{ccc}1 & 1 & 5 \ 2 & \lambda^2 & 9 \ 3 & \lambda & \mu\end{array}ight|=0 \Rightarrow \mu=13\end{aligned}$

Infinite solution $\lambda=1 \& \mu=13$

For unique $\operatorname{sol}^{\mathrm{n}} \lambda 
eq 1$

For no $\operatorname{sol}^{\mathrm{n}} \lambda=1 \& \mu 
eq 13$

If $\lambda 
eq 1$ and $\mu 
eq 13$

Considering the case when $\lambda=-\frac{1}{2}$ and $\mu 
eq 13$ this will generate no solution case

Consider the system of linear equations

$x+y+z=5, x+2 y+\lambda^2 z=9$

$x+3 y+\lambda z=\mu$, where $\lambda, \mu \in R$. Then, which of the following statement is NOT correct?

Similar Questions

For the system of linear equations $a x+y+z=1$, $x+a y+z=1, x+y+a z=\beta$, which one of the following statements is NOT correct ?

$\left| {\,\begin{array}{*{20}{c}}{19}&{17}&{15}\\9&8&7\\1&1&1\end{array}\,} \right| = $

If $a$, $b$, $c$, $d$, $e$, $f$ are in $G.P$., then the value of $\left| {\begin{array}{*{20}{c}}
{{a^2}}&{{d^2}}&x \\
{{b^2}}&{{e^2}}&y \\
{{c^2}}&{{f^2}}&z
\end{array}} \right|$ depends on

Evaluate the determinant $\Delta=\left|\begin{array}{rrr}1 & 2 & 4 \\ -1 & 3 & 0 \\ 4 & 1 & 0\end{array}\right|$

$\left| {\,\begin{array}{*{20}{c}}{1 + i}&{1 - i}&i\\{1 - i}&i&{1 + i}\\i&{1 + i}&{1 - i}\end{array}\,} \right| = $

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