srinivasanlsn said: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...
srinivasanlsn said:hmm ok atleast from the 4 options given , can u figure out the question ?? if its eigen value wat will be the ans ?
The algebraic multiplicity of a matrix is the number of times a particular eigenvalue appears as a root of the characteristic polynomial of the matrix. It is also equal to the degree of the corresponding eigenvalue in the characteristic polynomial.
The geometric multiplicity of a matrix is the number of linearly independent eigenvectors associated with a particular eigenvalue. The algebraic multiplicity is always greater than or equal to the geometric multiplicity, and they are equal if and only if the matrix is diagonalizable.
The algebraic multiplicity helps us understand the behavior of a matrix and its corresponding eigenvalues. It can also be used to determine if a matrix is diagonalizable, which has important implications in solving systems of linear equations and finding the eigenvalues and eigenvectors of a matrix.
The algebraic multiplicity can be calculated by finding the degree of the corresponding eigenvalue in the characteristic polynomial. This can be done by factoring the characteristic polynomial or by using the Cayley-Hamilton theorem.
No, the algebraic multiplicity cannot be greater than the dimension of the matrix. This is because the degree of the characteristic polynomial cannot be greater than the dimension of the matrix, and the algebraic multiplicity is equal to the degree of the corresponding eigenvalue in the characteristic polynomial.