Consider m 1 2 8 8 3 1 8 2 4 7 2 3 1 7 2 4 7 13 6 1 2 5 8 1

Consider m = [1 -2 -8 -8 -3 1 -8 -2 4 7 -2 3 1 7 -2 4 7 13 6 1 -2 -5 -8 1 4 0 -2 1 4 4 4 7 15 4 7 7 4 4 1 0 13 7 1 4 -5 1 -3 -2 4]Find its Jordan canonical form.

Solution

given that matrix M=[(1 -2 -8 -3 1 -8) (-2 4 7 -2 3 1 7) (-2 4 7 13 6 1 -2) (-5 -8 1 4 0 -2 1) (4 4 4 7 15 4 7) (7 4 4 1 0 13 7) (1 4 -5 1 -3 -2 4)]

(1)first this matrix is in trnsforme matrix.

(2)next we have to compute det(xI-A)

then,

det[(x-1 2 8 3 -1 8) (2 x-4 7 2 -3 -1- 7) (2 -4 x-7 -13 -6 -1 2) (5 8 -1 x-4 0 2 -1) -(4 -4 -4 -7 x-15 -4 -7) (-7 -4 -4 1 0 x-13 -7) (-1 -4 5 -1 --3 2 x-4)]

(x-1)det[ ( x-4 7 2 -3 -1- 7) ( -4 x-7 -13 -6 -1 2) ( 8 -1 x-4 0 2 -1) - -4 -4 -7 x-15 -4 -7) ( -4 -4 1 0 x-13 -7) ((4 5 -1 --3 2 x-4)]