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Homework Statement
Prove or disprove the title of this thread.
Homework Equations
AX=(lamda)X
The Attempt at a Solution
I don't know where to start
nicknaq said:Homework Statement
Prove or disprove the title of this thread.
Homework Equations
AX=(lamda)X
The Attempt at a Solution
I don't know where to start
Mark44 said:Start with the process you use to find the eigenvalues of a 3 x 3 matrix, which involves a determinant to get the characteristic equation for the matrix. What degree equation would you expect to get?
Mark44 said:So it's not possible for a 3 x 3 matrix to have four eigenvalues, right?
No, a 3x3 matrix can only have up to 3 distinct eigenvalues.
Yes, a 3x3 matrix can have complex eigenvalues, as long as it has at least one complex entry in its matrix elements.
You can find the eigenvalues of a 3x3 matrix by solving the characteristic equation, det(A-λI) = 0, where A is the matrix and λ is the variable representing the eigenvalue.
Yes, a 3x3 matrix can have repeated eigenvalues, as long as the matrix is not diagonalizable. In this case, the matrix will have fewer than 3 distinct eigenvalues.
A 3x3 matrix can have up to 3 linearly independent eigenvectors, corresponding to each of its eigenvalues.