Results 1 to 3 of 3

Math Help - Matrix characteristic equation help

  1. #1
    Junior Member
    Joined
    Apr 2008
    Posts
    72

    Matrix characteristic equation help

    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?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hello,

    Quote Originally Posted by deragon999 View Post
    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)
    Here is the mistake :

    It's ok for (3-x)((2-x)(3-x)-1)
    But the second term is -1((3-x){\color{red}-}0)

    --> \begin{aligned} f(x) &=(3-x)((2-x)(3-x)-1)-1(3-x) \\<br />
&=(3-x)(6-5x+x^2-2) \\<br />
&=(3-x)(4-5x+x^2) \\<br />
&=(3-x)(4-x)(1-x) \end{aligned}



    Also would the eigenvalues for the characteristic equation be 3, 4 and 1?
    Yes
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Apr 2008
    Posts
    72

    Tks

    Omg that makes me look like a dumbass after getting it right in the first half...
    neways thanks for ur help on both my latest questions..and many others besides.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: June 16th 2011, 07:32 AM
  2. Characteristic polynomial of a matrix
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: August 12th 2010, 01:56 AM
  3. Replies: 2
    Last Post: August 11th 2010, 04:26 AM
  4. Replies: 1
    Last Post: January 16th 2009, 09:07 PM
  5. Characteristic Polynomial from a matrix with an unknown...
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: November 10th 2007, 05:41 AM

Search Tags


/mathhelpforum @mathhelpforum