Let each matrix in Exercises 1–6 act on C2. Find the eigenvalues and a basis for each eigenspace in C2.

Solution 1EStep 1 Consider the matrix .The objective is to find the eigenvalues and a basis for each eigenspace in The characteristic equation of A is, Use the quadratic formula to find the eigenvalues: Therefore the eigenvalues are Step 2 Find the eigenvector corresponding to the eigenvalue Then, The above two equations determine the same relationship between The second equation leads to, .