Answer:
Step-by-step explanation:
Given matrix A is 2x2
A-kI =0 gives
[tex]\left[\begin{array}{ccc}2-k&1\\-1&2-k\end{array}\right] =0\\\\(2-k)^2+1=0\\2-k=i,-i\\k =2-i, 2+i[/tex]
Eigen values are 2-i, 2+i
a) k =2-i
[tex]\left[\begin{array}{ccc}i&1\\-1&i\end{array}\right] =0\\[/tex]
i.e. x1=ix2
OR Eigen vector is (i,1)
b) k =2+i
[tex]\left[\begin{array}{ccc}-i&1\\-1&-i\end{array}\right] =0\\[/tex]
i.e. x1=-ix2
OR Eigen vector is (-i,1)
