How to Determine the Eigenvalues of a Matrix


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What is the general equation we use to find the eigenvalues of any nxn matrix (A)?

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1. Let's say you work a problem where you find all the eigenvalues of a 5x5 matrix. How many eigenvalues will you find?

2. Find all the eigenvalues of the following 2x2 matrix (A).

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About This Quiz & Worksheet

To pass the quiz and worksheet you have to know how to find the eigenvalues of a given matrix. You must also know the way to determine how many eigenvalues can be found in a given matrix.

Quiz & Worksheet Goals

Questions test knowledge of:

  • Matrix multiplication
  • Vector multiplication
  • Finding an eigenvalue for a given matrix

Skills Practiced

  • Information recall - access the knowledge you've gained regarding the general equation for finding the eigenvalues of an 'n' x 'n' matrix
  • Reading comprehension - ensure that you draw the most important information from the lesson on eigenvalues
  • Knowledge application - use your knowledge to find the eigenvalues by solving a polynomial for its roots

Additional Learning

How to Determine the Eigenvalues of a Matrix is a lesson that will teach you more about eigenvalues. The objectives covered include the following:

  • Review the scaled version of a given vector
  • Understand the characteristic polynomial
  • Know the meaning of lambda