# Root and exponent of matrix

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1. May 24, 2015

### math 2015

1. The problem statement, all variables and given/known data
I. 3*3 matrix A (8 2 -2, 2 5 4, -2 4 5)

II. 3*3 matrix (1 2 0, -1 -2 0, 3 5 1)

2. Relevant equations
I. Solve Aexp 100 of 3*3
II. Find the 5th rooth of B matrix
3. The attempt at a solution
I. I got stuck at diagonalising the matrix. Is this OK 1st step ? If yes, what should I do next

II. Also here i started with diagonalising the matrix.

2. May 24, 2015

### hunt_mat

Diagonalising the matrix is the first step.

3. May 24, 2015

### vela

Staff Emeritus
What is this even supposed to mean? $Ae^{100}$? $A^{100}$?

4. May 24, 2015

### Ray Vickson

Or, perhaps, $e^{100A}$?

5. May 25, 2015

### math 2015

A100

6. May 25, 2015

### micromass

Staff Emeritus
OK, so what did you get for diagonalization? Where are you stuck trying to diagonalize it?

7. May 26, 2015

### math 2015

4 TIMES second row and 4 times 3rd row and distract from first row ?

8. May 26, 2015

### hunt_mat

1) Find the eigenvalues.
2) Find the eigenvectors

9. May 26, 2015

### math 2015

How ?

10. May 26, 2015

### HallsofIvy

Staff Emeritus
Seriously? You were given a problem like this and do not know how to find eigenvalues and eigenvectors? Do you know what "eigenvalues" and "eigenvectors" are? If not then I guess you will just have to start multiplying matrix A by itself!

11. May 26, 2015

### Staff: Mentor

@math 2015, if you do not know how to find eigenvalues and eigenvectors, crack open your textbook to find out how these operations are done. Your textbook should have several examples showing the steps. If you have any questions after you have done your reading, you can ask them here, but this forum is not intended to teach you how to carry out these operations.

12. May 26, 2015

### math 2015

I understand. What is the basic formula for calculating A100 finding the eigenvalues. Thank you all.I am new here. Do not be to harsh toward me. Thanks

13. May 26, 2015

### Staff: Mentor

Apparently you don't understand. What we're saying is that you need to start reading your textbook to find out how this is done. This process is more complicated than finding a formula and plugging in numbers.

14. May 26, 2015

### math 2015

eigen values are 0 and 9 (twice). can I found the A100 from diagonal matrix ?

15. May 26, 2015

### Ray Vickson

First of all, you need to determine IF the matrix is "diagonalizable". If you had three distinct eigenvalues, this would not be an issue, but when you have a repeated eigenvalue (as you do here), sometimes the matrix is diagonalizable, and sometimes not. What other information do you need to know in order to figure out whether the matrix is diagonalizable?

I would be willing to bet that this material is discussed in your textbook and/or course notes. People are suggesting that you actually read the material you have available; that is really the only way to learn.

If you do NOT have such material available to you (for some mysterious, hard-to-understand reason), please tell us. In that case we can suggest further on-line reading for you to pursue. Note, however, that our just telling you what formulas to use, etc., would not make sense: other writers/teachers have already written up this material and put it on line.