Solved: Let each matrix in Exercises act on 2. Find the

Solution 2EStep 1 Consider the matrix, The characteristics equation is, That is, Or, Or, Since the Eigen values are the roots of the characteristic equation,Therefore Eigen value is given by, Find Eigen vector corresponding to Eigen value ,Consider, So the equation gives, Now consider the augmented matrix, Apply row operations,In row2 multiply row2 by (2-i), In row2, subtract row1 from row2, This gives, Or, Here is a free variable.in particular take, This gives, So the Eigen vector for is given by, Next find Eigen vector corresponding to Eigen value ,So consider the equation, This gives, Consider the augmented matrix, Apply elementary row transformation,Multiply row2 by (2+i) gives, Now in row2 subtract row2 from row1, This gives, Or,