JEE Main Solved Paper 2017 Question 30
Question: If $ A \begin{bmatrix} 2 & -3 \\ -4 & 1 \\ \end{bmatrix} , $ then adj $ (3A^{2}+12A) $ is equal to:- [JEE Main Solved Paper-2017]
Options:
A) $ \begin{bmatrix} 72 & -63 \\ -84 & 51 \\ \end{bmatrix} $
B) $ \begin{bmatrix} 72 & -84 \\ -63 & 51 \\ \end{bmatrix} $
C) $ \begin{bmatrix} 51 & 63 \\ 84 & 72 \\ \end{bmatrix} $
D) $ \begin{bmatrix} 51 & 84 \\ 63 & 72 \\ \end{bmatrix} $
Show Answer
Answer:
Correct Answer: C
Solution:
Given $ A= \begin{bmatrix} 2 & -3 \\ -4 & 1 \\ \end{bmatrix} $
$ 3A^{2}= \begin{bmatrix} 16 & -9 \\ -12 & 13 \\ \end{bmatrix} $
$ 12A= \begin{bmatrix} 24 & -36 \\ -48 & 12 \\ \end{bmatrix} $
$ \therefore $ $ 3A^{2}+12A= \begin{bmatrix} 72 & -63 \\ -84 & 51 \\ \end{bmatrix} $
adj $ (3A^{2}+12A)= \begin{bmatrix} 51 & 63 \\ 84 & 72 \\ \end{bmatrix} $
