let M=[3,1,0;1,2,1;0,1,3] where ; specifies a new row

show that the characteristic equation is f(x)=(3-x)(x-4)(x-1)

Find det(M-xI) which is:

det[(3-x),1,0;1,(2-x),1;0,1,(3-x)]

=(3-x)((2-x)(3-x)-1)-1((3-x)(0)

=(3-x)(3-x)(2-x)-(3-x)

This expands to -x^3+8x^2-20x+15..which is not the same as the expanded form of the given equation..which is -x^3+8x^2-19x+12....

where have i gone wrong...

Also would the eigenvalues for the characteristic equation be 3, 4 and 1?