Search any question & find its solution
Question:
Answered & Verified by Expert
In the matrix $\left[\begin{array}{ccc}-1 & x & 3 \\ -4 & -5 & -6 \\ -7 & y & 9\end{array}\right]$, if the cofactors of -6 and -7 are respectively 22 and 27 , then $5 x+y=$
Options:
Solution:
1804 Upvotes
Verified Answer
The correct answer is:
-2
$\begin{aligned} & \text { } \mathrm{A}=\left[\begin{array}{ccc}-1 & \mathrm{x} & 3 \\ -4 & -5 & -6 \\ -7 & \mathrm{y} & 9\end{array}\right] \\ & \text { Here } \mathrm{A}_{23}=(-1)^{2+3}[-\mathrm{y}+7 \mathrm{x}]=(-1)(7 \mathrm{x}-\mathrm{y})=-7 \mathrm{x}+\mathrm{y} \\ & \Rightarrow-7 \mathrm{x}+\mathrm{y}=22 \\ & \Rightarrow \mathrm{A}_{31}=(-1)^{3+1}[-6 \mathrm{x}+15]=27 \\ & \Rightarrow-6 \mathrm{x}=12 \quad \Rightarrow \mathrm{x}=-2 \\ & \because \quad \text { From eq } \mathrm{eq}^{\mathrm{n}}(1) \quad(1) \\ & 14+\mathrm{y}=22 \Rightarrow \mathrm{y}=8 \\ & \text { Now } 5 \mathrm{x}+\mathrm{y}=5 \times(-2)+8=-2\end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.