E4out - Math 330 Exam 4 Outline Exam 4 for Math 330 will...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 330 Exam 4 Outline Exam 4 for Math 330 will take place on Friday April 17. Calculators will not be permitted. Eigenvalues - 15 points You be given a 3 3 matrix which has 3 distinct eigenvalues. The matrix will have sufficient zero entries so that the characteristic polynomial can be easily determined and factored. Here is an example: 1 A = 1 5 9 0 3 0 9 8 1 SOLUTION : det( A- I ) = vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle 1- 5 9 3- 9 8 1- vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle = (3- ) vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle 1- 9 9 1- vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle = (3- ) bracketleftBig (1- ) 2- 81 bracketrightBig = (3- ) bracketleftBig- 80- 2 + 2 bracketrightBig = (3- )( - 10)( + 8) So the eigenvalues are 3,10, and -8. Diagonalizable or Not - 15 points You will be given an n n matrix with n equal to 3,4, or 5. You will be told all the eigenvalues although the list of these will have length less than n . You job will be to decide if the matrix is diagonalizable. By looking at the dimensions of the various eigenspaces (and seeing if these add up to n or something less than n ) you can decide if the matrix is diagonalizable. Here are two examples using 3 3 matrices: 2 1. The following matrix has eigenvalues 1 and 3. Is it diagonalizable?1....
View Full Document

Page1 / 4

E4out - Math 330 Exam 4 Outline Exam 4 for Math 330 will...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online