NDA 2015
- Exam
- NDA
- Year
- 2015
- Subject
- Mathematics
- Chapter
- Matrices
NDA 2015 · Mathematics · Matrices
If A=[ array ll 2 & 7 1 & 5 array ] then that is A+3 A^ -1 equal...
If A=\left[\right] then that isA+3 A^{-1}I is the identity matrix order 2.
Options
- A
- B
- C
- DNone of these
Correct answer
C.
Step-by-step solution
A=\left[\right]
Now, $\begin{aligned} \Rightarrow & 3 \mathrm{ A}^{-1}=\left[\begin{array}{cc}5 & -7 \\ -1 & 2\end{array}\right] \\ & \text{Now, } A+3 \mathrm{ A}^{-1}=\left[\begin{array}{ll}2 & 7 \\ 1 & 5\end{array}\right]+\left[\begin{array}{cc}5 & -7 \\ -1 & 2\end{array}\right] \\ \quad & =\left[\begin{array}{ll}7 & 0 \\ 0 & 7\end{array}\right]=7\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]=7 I \text{ where } I \text{ is Identity Matrix. }\end{aligned}