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NDA 2010
Exam
NDA
Year
2010
Subject
Mathematics
Chapter
Matrices

NDA 2010 · Mathematics · Matrices

Let A=[ array ll 1 & 2 3 & 4 array ]=[a_ i j ] , where i, j,=1,2 ....

Let \mathrm{A}=\left[1234\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]=\left[a_{i j}\right], where i,j,=1,2i, j,=1,2. If its inverse matrix is \left[b_{i j}\right],whatis, what isb_{22}$ ?

Options

  1. A-2
  2. B1
  3. C32\frac{3}{2}
  4. D−12-\frac{1}{2}

Correct answer

D. −12-\frac{1}{2}

Step-by-step solution

∣A∣=4−6=−2A−1=[bij]=1−2[4−2−31]=[−2132−12]\begin{aligned} & |\mathrm{A}|=4-6=-2 \\ & \mathrm{ A}^{-1}=\left[\mathrm{b}_{\mathrm{ij}}\right]=\frac{1}{-2}\left[\begin{array}{cc}4 & -2 \\ -3 & 1\end{array}\right]=\left[\begin{array}{cc}-2 & 1 \\ \frac{3}{2} & -\frac{1}{2}\end{array}\right]\end{aligned}\therefore \mathrm{b}_{22}=-\frac{1}{2}$
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