Calculating Eigenvalues and Eigenvectors

In summary, the question initially had an error in the second term, which should have been De^( - √(5)t). After correcting this, the calculations were worked out to be A = 0, B = -1/5, C = 3/10, D = -3/10, with the final answer being 3.09. The person just wanted to confirm if their solution was correct.
  • #1
dvep
43
0

Homework Statement



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.

The Attempt at a Solution



I worked it out to be

A = 0, B = -1/5, C = 3/10, D = -3/10

answer is 3.09

Is that correct? I have been through my calculations and can find no fault, I just want to make sure I have a good grasp on these questions, thank you.
 
Last edited:
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  • #2
The link takes me to a moved/deleted picture.
 
  • #3
gb7nash said:
The link takes me to a moved/deleted picture.

Sorry, I have fixed it now, thanks.
 

FAQ: Calculating Eigenvalues and Eigenvectors

1. What are eigenvalues and eigenvectors?

Eigenvalues and eigenvectors are mathematical concepts used to describe the behavior of linear transformations. Eigenvalues are a set of scalar values that represent the scaling factor of the eigenvectors when they are transformed by a given linear transformation. Eigenvectors are the corresponding non-zero vectors that are scaled by the eigenvalues.

2. What is the importance of eigenvalues and eigenvectors?

Eigenvalues and eigenvectors are important in many fields, including physics, engineering, and computer science. They are used to analyze the behavior of complex systems and to identify key features of the system. They also have practical applications, such as in data compression and image processing.

3. How are eigenvalues and eigenvectors calculated?

To calculate eigenvalues and eigenvectors, we use the characteristic equation for a given linear transformation. This equation is solved to find the eigenvalues, which are then used to find the corresponding eigenvectors. The process involves finding the roots of a polynomial equation and solving a system of linear equations.

4. Can a matrix have more than one eigenvalue and eigenvector?

Yes, a matrix can have multiple eigenvalues and eigenvectors. However, the number of eigenvalues is always equal to the number of dimensions of the matrix. This means that a 3x3 matrix can have a maximum of three eigenvalues and eigenvectors.

5. What is the relationship between eigenvalues and eigenvectors?

The relationship between eigenvalues and eigenvectors is that the eigenvalues determine the scaling factor of the eigenvectors when they are transformed by a linear transformation. This means that the eigenvectors are transformed along the same direction as the original vector, but their magnitude is changed by the eigenvalue.

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