4. Let A be the 6*6 diagonal matrix below. For each eigenvalue,compute the multiplicity of ? as a root of the characteristicpolynomial and compare it to the dimension of the eigenspaceE?.
(x 0 0 0 0 0 0 x 0 0 0 0 0 0 y 0 0 0 0 0 0 x 0 0 0 0 0 0 z 0 0 00 0 0 x)
5. Let A be an 3*3 upper triangular matrix with all diagonalelements equal, such as (3 4 -2 0 3 12 0 0 3) Prove that A isdiagonalizable if and only if A is a scalar times the identitymatrix.
