Matrix A is factored in the form PDP^-1. Use the Diagonalization Theorem to find
ID: 3109151 • Letter: M
Question
Matrix A is factored in the form PDP^-1. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. A = [2 0 -8 8 6 16 0 0 6] = [-2 0 -1 0 1 2 1 0 0][6 0 0 0 6 0 0 0 2] [0 0 1 2 1 4 -1 0 -2] Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed) A. There is one distinct eigenvalue, lambda =. A basis for the corresponding eigenspace is {}. B. In ascending order, the two distinct eigenvalues are lambda_1 = and lambda_2 =. Bases for the corresponding eigenspaces are {} and {}, respectively. C. In ascending order, the three distinct eigenvalues are lambda_1 =, lambda_2 =, and lambda_3 =. Bases for the corresponding eigenspaces are {}, {}, and {}, respectively.Explanation / Answer
By Diagonisable theorem
A=PDP-1
where p is the matrix whose column are the eigen vector
and D is the diagonal matrix whose diagonal are the eigen value
thus comparing with given value
eigen values are 2, 6 , 6 in ascending order
and corresponding eigen vector are {-2 0 1} {0 1 0} and {-1 2 0}