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Engineering Mathematics Question on Eigenvectors

The eigenvectors of the matrix are:
A=(i1 2−i)A=\left(\begin{matrix} i & 1 \\\ 2 & -i \end{matrix}\right)

A

{(1 1−i),(1 1+i)}\begin{Bmatrix} \left(\begin{matrix} 1 \\\ 1-i \end{matrix}\right),\left(\begin{matrix} 1 \\\ 1+i \end{matrix}\right) \end{Bmatrix}

B

{(i 1−i),(1 −1−i)}\begin{Bmatrix} \left(\begin{matrix} i \\\ 1-i \end{matrix}\right),\left(\begin{matrix} 1 \\\ -1-i \end{matrix}\right) \end{Bmatrix}

C

{(1+i −1),(1 1+i)}\begin{Bmatrix} \left(\begin{matrix} 1+i \\\ -1 \end{matrix}\right),\left(\begin{matrix} 1 \\\ 1+i \end{matrix}\right) \end{Bmatrix}

D

{(2+i 1),(1 3−i)}\begin{Bmatrix} \left(\begin{matrix} 2+i \\\ 1 \end{matrix}\right),\left(\begin{matrix} 1 \\\ 3-i \end{matrix}\right) \end{Bmatrix}

Answer

{(i 1−i),(1 −1−i)}\begin{Bmatrix} \left(\begin{matrix} i \\\ 1-i \end{matrix}\right),\left(\begin{matrix} 1 \\\ -1-i \end{matrix}\right) \end{Bmatrix}

Explanation

Solution

The correct option is(B): {(i 1−i),(1 −1−i)}\begin{Bmatrix} \left(\begin{matrix} i \\\ 1-i \end{matrix}\right),\left(\begin{matrix} 1 \\\ -1-i \end{matrix}\right) \end{Bmatrix}