\(\begin{aligned} &\text { If system of equations }\\ &\begin{aligned} & x+2 y-3 z=2 \\ & 2 x+\lambda y+…
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\(\begin{aligned}
&\text { If system of equations }\\
&\begin{aligned}
& x+2 y-3 z=2 \\
& 2 x+\lambda y+5 z=5 \\
& 4 x+3 y+\mu z=33 \text { has infinite solutions, then } \lambda+\mu \text { is equal to }
\end{aligned}
\end{aligned}\)
✓ Correct answer: a)
\( \frac{1334}{5}\)
Explanation
Ans. (2)
Sol.
\(\begin{aligned}
& \Delta=\left|\begin{array}{lll}
1 & 2 & -3 \\
2 & \lambda & 5 \\
4 & 3 & \mu
\end{array}\right|=0 \\
& 12 \lambda+\lambda \mu-4 \mu+7=0\ldots \ldots (i) \\
& \Delta z=\left|\begin{array}{lll}
1 & 2 & 2 \\
2 & \lambda & 5 \\
4 & 3 & 33
\end{array}\right|=0 \\
& \lambda=\frac{19}{5} \\
& \text { from (i) } \mu=263 \\
& \lambda+\mu=\frac{19}{5}+263=\frac{1334}{5}
\end{aligned}\)
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