# Thread: Matrix help

1. ## Matrix help

A =$\displaystyle \begin{bmatrix} 1 & 1 & 0 \\0 & 2 & 1 \\-4 & -11 & -4 \end{bmatrix}$

find the smallest value of n > 0 such that

I need help on this question, I am suppose to solve it using matlab, however, I dont even know how to solve this on paper, let alone matlab, any suggestions or help appreciated.

I have tried to to it like this

$\displaystyle A^{-1}A^{n} =IA^{-1}$

$\displaystyle n = IA^{-1}$
to get n, and matlab gives me,

$\displaystyle \begin{bmatrix} -3 & -4 & -1 \\4 & 4 & 1 \\-8 & -7 & -2 \end{bmatrix}$

so is n = 1? Is this correct?

2. ## Re: Matrix help

Originally Posted by Tweety
A =$\displaystyle \begin{bmatrix} 1 & 1 & 0 \\0 & 2 & 1 \\-4 & -11 & -4 \end{bmatrix}$

find the smallest value of n > 0 such that

I need help on this question, I am suppose to solve it using matlab, however, I dont even know how to solve this on paper, let alone matlab, any suggestions or help appreciated.

I have tried to to it like this

$\displaystyle A^{-1}A^{n} =IA^{-1}$

$\displaystyle n = IA^{-1}$
to get n, and matlab gives me,

$\displaystyle \begin{bmatrix} -3 & -4 & -1 \\4 & 4 & 1 \\-8 & -7 & -2 \end{bmatrix}$

so is n = 1? Is this correct?

Hi Tweety!

If you fill in n=1, you'll get $\displaystyle A^n = A^1 = A$.
That does not look like the identity matrix.
So no, it is not n=1.

If you're using matlab you might simply iterate over n, calculate A^n and see if it matches the identity matrix.

Using a little math would be to calculate the eigenvalues.
If any of them has an absolute value that deviates from 1, it is not possible.
Then you need to find the lowest integer power that will turn all eigenvalues into 1.
If there is one, that is your prime candidate.
You will still have to verify if it fits.

3. ## Re: Matrix help

Thank you, but still slightly confused...

I defined my matrix in matlab, and calculated a^n , for different values of n, 1,2,3 etc... but get no where near the idenity matrix

4. ## Re: Matrix help

Actually I just tried a^4 and got the indenity matrix, thank you sooo much