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Algebraic multiplicity of matrix

  1. Apr 3, 2012 #1
    hi friends plz help in finding out the ans for this . A 3x3 matrix was given , am asked to find algebraic multiplicity of it !! how to find algebraic multiplicity of 3x3 matrix ??
     
  2. jcsd
  3. Apr 3, 2012 #2

    micromass

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    Did you mean the algebraic multiplicity of an eigenvalue??

    Well, how did you define it??
     
  4. Apr 12, 2012 #3
    the algebraic multiplicity of the matrix a=[ 0 1 0 ]
    [ 0 0 1 ]
    [ 1 -3 3 ]
    a.1
    b.2
    c.3
    d.4

    i don get the question first, somebody help me...
     
  5. Apr 12, 2012 #4
    my next question is how to find determinant of 4x4 matrix ??
     
  6. Apr 15, 2012 #5
    the algebraic multiplicity of the matrix
    [ 0 1 0 ]
    [ 0 0 1 ]
    [ 1 -3 3 ]

    options :
    a.1
    b.2
    c.3
    d.4

    i don get the question first, somebody help me...
     
  7. Apr 15, 2012 #6

    micromass

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    Again, what is your definition of algebraic multiplicity?
     
  8. Apr 24, 2012 #7
    First rearrange and the answer is obvious.

    [1 -3 3]
    [0 1 0]
    [0 0 1]

    From here the eigenvalues are obviously [1,1,1]. From here the question says what is the algebraic multiplicity. The question was obviously used for simplicity, so you know the multiplicity for the eigenvalue 1 is 3 since it appears in the diagonal 3 times.

    Since it is the only one the answer can only be C.
     
  9. Apr 25, 2012 #8

    AlephZero

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    We know what the algebraic multiplicity of an eigenvalue is.

    The OP's question was about the algebraic multiplicity of a matrix, which is not a term that I have ever seen before (and neither has Google).

    Maybe something got "lost in tanslation" here...
     
  10. Apr 25, 2012 #9

    HallsofIvy

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    To find the determinant of a 4x4 matrix, you could use the basic definition- but that's very difficult. Most people use "expansion by minors".
    The determinant of
    [tex]\left|\begin{array}{cccc}a & b & c & d \\ e & f & g & h \\ i & j & k & l\\ m & n & o & p\end{array}\right|[/tex]
    is given by
    [tex]a\left|\begin{array}{ccc}f & g & h \\ j & k & l \\ n & o & p\end{array}\right|- b\left|\begin{array}{ccc}e & g & h \\ i & k & l \\ m & o & p\end{array}\right|+ c\left|\begin{array}{ccc}e & f & h \\ i & j & l\\ m & n & p\end{array}\right|- d\left|\begin{array}{ccc}e & f & g \\ i & j & k \\ n & o & p \end{array}\right|[/tex]
     
  11. Apr 25, 2012 #10
    AlephZero & srinivasanlsn,

    Remember this post shows that the person asking is answering a multiple choice question, as everyone is aware, which has a common instructor imposed complication written in, which is: as you mentioned a term which has no direct definition but instead must be understood only be really understanding the term multiplicity as it is used in Linear algebra.

    The multiplicity of an eigenvalue λ of a linear transformation T as the number of independent associated eigenvectors. That is, as the dimension of the kernel of T-λ1V. etc, etc...

    If the student knows this or something similar then the seemingly confusing terminology is made clear by using the terms interchangeably due to a nesting effect of definitions. Much like the use of dimension of the kernel above could be stated in a more confusing manner like using it to ask the question: what is the dimension of the kernel for A=.....

    Not preaching, as nearly all people answering questions knows this already, just telling the person asking to look through the questions by understanding the definitions better.
     
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