fzero said:It's correct. though it's possible that they want an exact expression instead of a numerical approximation.
dvep said:thank you for your reply, that is good to hear.
Could you also check this one http://i1225.photobucket.com/albums/ee382/jon_jon_19/Eigen2.jpg
The second term should be De^( - √(5)t), I made a mistake when writing out the question.
Just want to make sure i got a good grasp of this, my answer is 3.09
thank you
Eigenvalues and eigenvectors are important concepts in linear algebra that are used to understand the behavior of linear transformations. Eigenvalues represent the scale factor by which an eigenvector is stretched or compressed when transformed by a matrix.
To find eigenvalues and eigenvectors, you need to set up and solve an eigenvalue equation. This involves finding the characteristic polynomial of the matrix and solving for the roots, which are the eigenvalues. Then, the corresponding eigenvectors can be found by solving a system of linear equations.
Eigenvalues and eigenvectors are important because they help us understand the behavior of linear transformations, which have many real-world applications. They also allow us to simplify complex systems and make calculations easier.
Yes, a matrix can have multiple eigenvalues and corresponding eigenvectors. The number of eigenvalues and eigenvectors depends on the size and properties of the matrix.
Eigenvalues and eigenvectors are used in data analysis to reduce the dimensionality of a dataset and extract important patterns and trends. They are also used in techniques such as principal component analysis to transform data into a new coordinate system that better represents the data.