# algebraic multiplicity of matrix

by srinivasanlsn
Tags: algebraic, matrix, multiplicity
 P: 6 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 ??
 Emeritus Sci Advisor Thanks PF Gold P: 15,867 Did you mean the algebraic multiplicity of an eigenvalue?? Well, how did you define it??
 P: 6 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...
P: 6

## algebraic multiplicity of matrix

my next question is how to find determinant of 4x4 matrix ??
 P: 6 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...
 Emeritus Sci Advisor Thanks PF Gold P: 15,867 Again, what is your definition of algebraic multiplicity?
 P: 2 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.
 Engineering Sci Advisor Thanks P: 6,031 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...
Math
Emeritus
$$\left|\begin{array}{cccc}a & b & c & d \\ e & f & g & h \\ i & j & k & l\\ m & n & o & p\end{array}\right|$$
$$a\left|\begin{array}{ccc}f & g & h \\ j & k & l \\ n & o & p\end{array}\right|- b\left|\begin{array}{ccc}e & g & h \\ i & k & l \\ m & o & p\end{array}\right|+ c\left|\begin{array}{ccc}e & f & h \\ i & j & l\\ m & n & p\end{array}\right|- d\left|\begin{array}{ccc}e & f & g \\ i & j & k \\ n & o & p \end{array}\right|$$