If the system of equations
$$
\begin{aligned}
& x+2 y-3 z=2 \\
& 2 x+\lambda y+5 z=5 \\
& 14 x+3 y+\mu z=33
\end{aligned}
$$
has infinitely many solutions, then $\lambda+\mu$ is equal to :
Solution
<p>$$\begin{aligned}
&\begin{aligned}
& \mathrm{D}=\left|\begin{array}{rrr}
1 & 2 & -3 \\
2 & \lambda & 5 \\
14 & 3 & \mu
\end{array}\right|=0, \lambda \mu+42 \lambda-4 \mu+107=0 \\
& \mathrm{D}_1=2 \lambda \mu+99 \lambda-10 \mu+255 \\
& \mathrm{D}_2=13-\mu \\
& D_3=5 \lambda+5 \\
& D_2=0 \Rightarrow \mu=13 \& D_3=0 \Rightarrow \lambda=-1
\end{aligned}\\
&\text { check & verify for these values } \mathrm{D} \& \mathrm{D}_2=0
\end{aligned}$$</p>
About this question
Subject: Mathematics · Chapter: Matrices and Determinants · Topic: Types of Matrices and Operations
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