If the system of equations, 2 x + 7 y + z = 3 , 3 x + 2 y + 5 z = 4 , x + y + 32 z = - 1 has infinitely many solutions, then is equal to _______. [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.
If the system of equations, $2 x + 7 y + λ z = 3,$ $3 x + 2 y + 5 z = 4,$ $x + μ y + 32 z = - 1$ has infinitely many solutions, then $(λ - μ)$ is equal to _______. [2024]

Ans.
(38)

Given, $2 x + 7 y + λ z = 3$

$3 x + 2 y + 5 z = 4$

$x + μ y + 32 z = - 1$ has infinitely many solutions.

$\Rightarrow Δ = 0, Δ_{1} = 0, Δ_{2} = 0$ and $Δ_{3} = 0$

$Δ_{2} =$ $| \begin{matrix} 2 & λ & 3 \\ 3 & 5 & 4 \\ 1 & 32 & - 1 \end{matrix} |$ $= 0$ and $Δ_{3} =$ $| \begin{matrix} 2 & 7 & 3 \\ 3 & 2 & 4 \\ 1 & μ & - 1 \end{matrix} |$ $= 0$

$\Rightarrow - 266 + λ (7) + 273 = 0$ and $- 4 - 8 μ + 49 + 9 μ - 6 = 0$

$\Rightarrow 7 λ + 7 = 0$ and $μ + 39 = 0$

$\Rightarrow λ = - 1$ and $μ = - 39$

So, $λ - μ = - 1 + 39 = 38$

Want Us to Email you About Special Offers & Updates?