Depending upon the numbers you are given, the matrix in this problem might have a characteristic polynomial that is not feasible to factor by hand without using methods from precalculus such as the rational root test and polynomial division. On an exam, you are expected to be able to find eigenvalues using cofactor expansions for matrices of size 3 x 3 or larger, but we will not expect you to go the extra step of applying the rational root test or performing polynomial division on Math 1553 exams. With this in mind, if you are unable to factor the characteristic polynomial in this particular problem, you may use a calculator or computer algebra system to get the eigenvalues. The matrix -4 -2 14 1 -1 0 1 A= 2 -2 -1 0 0 0 0 0 has two real eigenvalues li < 12. Find these eigenvalues, their multiplicities, and the dimensions of their corresponding eigenspaces. The smaller eigenvalue li = has algebraic multiplicity and the dimension of its corresponding eigenspace is The larger eigenvalue 12 = has algebraic multiplicity and the dimension of its corresponding eigenspace is Do the dimensions of the eigenspaces for A add up to the number of columns of A? choose v Note: You can earn partial credit on this problem