bmb2009 said:Homework Statement
Calculate the eigenvalues of the matrix
5 2
-3 0
Homework Equations
The Attempt at a Solution
Ok we were taught that eigenvalues were calculated by taking the determinant( A - λI) = 0. So just subtract a "λ" value from the diagnol entries of the given matrix... so why aren't the eigenvalues 5 and 0? Please help me understand why the e values are 2 and 3?
I have to ask: Why do you think the eigenvalues would be 5 and 0?bmb2009 said:Ok we were taught that eigenvalues were calculated by taking the determinant( A - λI) = 0. So just subtract a "λ" value from the diagnol entries of the given matrix... so why aren't the eigenvalues 5 and 0? Please help me understand why the e values are 2 and 3?
To calculate eigenvalues, you first need to find the determinant of the matrix. Then, you need to solve for the roots of the characteristic polynomial to obtain the eigenvalues.
Eigenvalues represent the scaling factor of the corresponding eigenvector in a matrix transformation. They provide important information about the properties and behavior of the matrix, such as its stability and invertibility.
Eigenvectors are the non-zero vectors that remain in the same direction after being transformed by a matrix. They are associated with eigenvalues and are crucial for understanding the behavior of a matrix.
A matrix will have complex eigenvalues if its characteristic polynomial has complex roots. This can be determined by finding the discriminant of the polynomial, which will be negative for complex roots.
Yes, eigenvalues have various applications in fields such as physics, engineering, and computer science. They are used in data analysis, image compression, and signal processing, among others.