How Do You Calculate Matrix Powers and Roots?

[math 2015]

Homework Statement

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)

Homework Equations

I. Solve Aexp 100 of 3*3
II. Find the 5th rooth of B matrix

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.

 

[hunt_mat]

Diagonalising the matrix is the first step.

 

[vela]

Homework Statement

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)

Homework Equations

I. Solve Aexp 100 of 3*3

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

II. Find the 5th rooth of B matrix

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.

 

[Ray Vickson]

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

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

 

[math 2015]

A¹⁰⁰

 

[micromass]

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

 

[math 2015]

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

 

[hunt_mat]

1) Find the eigenvalues.
2) Find the eigenvectors

 

[math 2015]

How ?

 

[HallsofIvy]

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!

 

[Mark44]

How ?

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!

@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.

 

[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

 

[Mark44]

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

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.

 

[math 2015]

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

 

[Ray Vickson]

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

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.