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characteristic polynomial for a 3x3 matrix

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an algorithm to generate the

characteristic polynomial

for a 3x3 matrix

M

M

det M

The constant term is

minus the determinant

of the matrix M.

M

trace M

det M

The coefficient of the 2 term is minus

the trace of the matrix M .

The trace of the matrix M = a + e + i.

M

trace M

det M

The coefficient of the term is:

+

M

trace M

det M

The coefficient of the term is:

+

+

M

trace M

det M

The coefficient of the term is:

+

+

example:

M

det M = 45

The constant term is

minus the determinant

of the matrix M =45

M

trace M=11

45

The coefficient of the 2 term is minus

the trace of the matrix M .

The trace of the matrix M = a + e + i = 11

M

11

45

The coefficient of the term is:

+

M

11

45

The coefficient of the term is:

9

+

+

M

11

45

The coefficient of the term is:

9

9

+

+

M

39

11

45

The coefficient of the term is:

9

9

21

+

+

M

39

11

45