Question

The values of $\lambda$ and $\mu$ for which the system of linear equations
$x+y+z=2$
$x+2 y+3 z=5$
$x+3 y+\lambda z=\mu$
has infinitely many solutions are, respectively

• A. 5 and 7
• B. 6 and 8
• C. 4 and 9
• D. 5 and 8

Answer 1

Answer: (D)

For infinite many solutions
$D = D _{1}= D _{2}= D _{3}=0$
Now $D=\begin{vmatrix}1&1&1\\ 1&2&3\\ 1&3&\lambda\end{vmatrix}=0$
$1 .(2 \lambda-9)-1 .(\lambda-3)+1 .(3-2)=0$
$\therefore \lambda=5$
Now $D_{1}=\begin{vmatrix}2&1&1\\ 5&2&3\\ \mu&3&5\end{vmatrix}=0$
$2(10-9)-1(25-3 \mu)+1(15-2 \mu)=0$
$\mu=8$