1. ## Compute S^k

$\textsf{Let:}$

$$S=\left[\begin{array}{rrrrrr} 0& 1& 0& 0&0\\ 0& 0& 1& 0&0\\ 0& 0& 0&1&0\\0&0&0&0&0 \end{array}\right]$$

$Compute \, S^k k=2,...,6$

$\text{ok we are supposed to do this with SAGE}$

$\text{but not sure how$S^k$is applied}$

2. ## Re: Compute S^k

Again, I have no idea what "SAGE" is! However, I strongly suggest that you go back and check the statement of the problem. The matrix you show has 5 columns and only 4 rows. It cannot be multiplied by itself!

3. ## Re: Compute S^k

why can we not remove $\displaystyle c_1,r_4,c_5$

4. ## Re: Compute S^k

Originally Posted by bigwave
why can we not remove $\displaystyle c_1,r_4,c_5$
What does that mean? I do not recognize your notation. I am guessing here, but are you suggesting that you remove columns 1 and 5 and row 4? You cannot remove them because they are in the matrix. You would have a different matrix if you removed them. And, if you remove two columns and one row, you would still not have a square matrix.

Whatever rules you are using to determine what you can and cannot do with matrices are not rules of linear algebra. People on this forum keep telling you that we are not familiar with SAGE. I would recommend moving this question to a discussion board that is specific to SAGE. Because what you are suggesting is not a differential equations problem.

5. ## Re: Compute S^k

there is no linear algebra catagory here.

6. ## Re: Compute S^k

I'm assuming there is a Diffeq relation to this?

-Dan

7. ## Re: Compute S^k

ok, there was a error in the handout so it was corrected to a 5x5 matrix
this was done in Cocalc

8. ## Re: Compute S^k

Originally Posted by bigwave
ok, there was a error in the handout so it was corrected to a 5x5 matrix
this was done in Cocalc

now that you have a square matrix as far as I can tell the entire exercise is to write a simple loop that repeatedly multiples this matrix by itself and prints the answer.

A quick gloss over the SAGE doc shows that this is pretty trivial to do.

What exactly do you need help with?