engineering recuitment GATE ECE 2023-24 Test Series Engineering Mathematics Linear Algebra Eigenvectors
For a given 2 × 2 matrix A, it is observed that \({\rm{A}}\left[ {\begin{array}{*{20}{c}} { - 1}\\ 1 \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} { - 1}\\ 1 \end{array}} \right]{\rm{\;and\;A}}\left[ {\begin{array}{*{20}{c}} { - 1}\\ 2 \end{array}} \right] = 2\left[ {\begin{array}{*{20}{c}} 1\\ { - 2} \end{array}} \right]\)
The matrix A is:
1
\(A = \left[ {\begin{array}{*{20}{c}}
{ - 1}&{ - 1}\\
{ - 1}&{ - 2}
\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
1&0\\
0&{ - 2}
\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
{ - 2}&{ - 1}\\
1&1
\end{array}} \right]\)
2
\(A = \left[ {\begin{array}{*{20}{c}}
{ - 1}&{ - 1}\\
1&2
\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
1&0\\
0&{ - 2}
\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
{ - 2}&{ - 1}\\
1&1
\end{array}} \right]\)
3
\(A = \left[ {\begin{array}{*{20}{c}}
{ - 1}&{ - 1}\\
1&2
\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
1&0\\
0&{ - 2}
\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
2&1\\
{ - 1}&{ - 1}
\end{array}} \right]\)
4
\(A = \left[ {\begin{array}{*{20}{c}}
{ - 1}&1\\
1&2
\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
1&0\\
0&2
\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
{ + 2}&1\\
{ - 1}&{ - 1}
\end{array}} \right]\)