QJEEM20Mab5a3: JEE Main 2020 Mathematics - Class 12 JEEM20Mab5a3 Solution: The values of and for which the system of linear equations x +…

Question

Verified Solution • 2025–26 Session moderate

The values of

\lambda

and

\mu

for which the system of linear equations
x + y + z = 2
x + 2y + 3z = 5
x + 3y +

\lambda

z =

\mu

has infinitely many solutions are, respectively:

Accepted Answer

For infinite many solutions

D = D₁ = D₂ = D₃ = 0

Now D =

| \begin{matrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & λ \end{matrix} |

= 0

\Rightarrow

1. (2

\lambda

– 9) –1.(

\lambda

– 3) + 1.(3 – 2) = 0

\Rightarrow

\lambda

= 5

Now D₁ =

| \begin{matrix} 2 & 1 & 1 \\ 5 & 2 & 3 \\ μ & 3 & 5 \end{matrix} |

= 0

\Rightarrow

2(10 – 9) –1(25 – 3

\mu

) + 1(15 – 2

\mu

) = 0

\Rightarrow

\mu

= 8

Step-by-Step Verified Solution