Consider the system of linear equations x + y + z = 5 , x + 2 y + 2 z = 9 , x + 3 y + z = , where. Then which of the following statement is NOT correct? [2024]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
Consider the system of linear equations $x + y + z = 5,$ $x + 2 y + λ^{2} z = 9,$ $x + 3 y + λ z = μ,$ where $λ, μ \in R .$ Then which of the following statement is NOT correct [2024]

1 System has unique solution if $λ \neq 1$ and $μ \neq 13$ .

2 System is inconsistent if $λ = 1$ and $μ \neq 13 .$

3 System is consistent if $λ \neq 1$ and $μ = 13 .$

4 System has infinite number of solutions if $λ = 1$ and $μ = 13 .$

Ans.
(1)

$| \begin{matrix} 1 & 1 & 1 \\ 1 & 2 & λ^{2} \\ 1 & 3 & λ \end{matrix} |$ $= 0 \Rightarrow 2 λ^{2} - λ - 1 = 0$

$\Rightarrow λ = 1, - \frac{1}{2} and$ $| \begin{matrix} 1 & 1 & 5 \\ 2 & λ^{2} & 9 \\ 3 & λ & μ \end{matrix} |$ $= 0 \Rightarrow μ = 13$

For infinite solution, $λ = 1$ and $μ = 13$

For unique solution $λ \neq 1$

For no solution, $λ = 1$ and $μ \neq 13$

If $λ \neq 1$ and $μ \neq 13$

Considering the case when $λ = - \frac{1}{2}$ and $μ \neq 13$ this will generate no solution case.

Want Us to Email you About Special Offers & Updates?