ISRO-2013-33

Question

What is the matrix transformation which takes the independent vectors $\begin{pmatrix}
1& \\
2& 
\end{pmatrix}$ and $\begin{pmatrix}
2& \\
5& 
\end{pmatrix}$ and transforms them to $\begin{pmatrix}
1& \\
1& 
\end{pmatrix}$ and $\begin{pmatrix}
3& \\
2& 
\end{pmatrix}$ respectively?

• A. $\begin{pmatrix}
  1&-1 \\
  1& 0
  \end{pmatrix}$
• B. $\begin{pmatrix}
  0&0 \\
  0.5& 0.5
  \end{pmatrix}$
• C. $\begin{pmatrix}
  -1&0 \\
  1& 1
  \end{pmatrix}$
• D. $\begin{pmatrix}
  -1&1 \\
  1& 0
  \end{pmatrix}$

Answer 1

option D

Comments

please correct if any mistakes

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Now it is nice one.

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nice

 

Answer 2

$A\begin{pmatrix}  1&2 \\2& 5    \end{pmatrix}=   \begin{pmatrix}  1&3 \\1& 2    \end{pmatrix}$

$\begin{pmatrix}  1&2 \\2& 5    \end{pmatrix}^{-1} = \begin{pmatrix}  5&-2 \\-2& 1    \end{pmatrix}$

Therefore $A=\begin{pmatrix}  1&3 \\1& 2    \end{pmatrix}\begin{pmatrix}  5&-2 \\-2& 1    \end{pmatrix} = \begin{pmatrix}  -1&1 \\1& 0    \end{pmatrix}$

Answer 3

Refer this