Find h such that the matrix 4 0 0 0 2 2 0 0 3 h 4 0 3 3 14 2

Find h such that the matrix [4 0 0 0 2 2 0 0 3 h 4 0 3 3 14 2] has a two-dimensional eigenspace for lambda = 4 is two-dimensional. What dimension is the eigenspace if h does not take on this value?

Solution

eigen value = 4 for givrn matrix

det(A -4I) =0;

for eigen value = 4 for every value of h this matrix can have eigen value =4