Matrix^17 X vector and limit demonstraction

[kikofra]

Hi,
in my last exam, i failed to solve this problem, and im trying and trying and i cannot solve it:

Matrix A=( 1 2/3) ,vector X1=(-1) and vector X2=(2/3).
(1 3/2) ( 1) (1 )

a) Find a expression to A¹⁷ X1
b)Find a expression to A²³ X2
c) show that not exist t e R such that (a)= tX1, so lim k--->|ak|= +oo = lim k---->|bk|, where (a_{k)= A^k} (a)
(b) (b_{k) (b)}

I have some trouble to put the matrixs into the text, sorry

Thank you in advance for help:grin:

 

[Ishuda]

Hi,
in my last exam, i failed to solve this problem, and im trying and trying and i cannot solve it:

Matrix A=( 1 2/3) ,vector X1=(-1) and vector X2=(2/3).
(1 3/2) ( 1) (1 )

a) Find a expression to A¹⁷ X1
b)Find a expression to A²³ X2
c) show that not exist t e R such that (a)= tX1, so lim k--->|ak|= +oo = lim k---->|bk|, where (a_{k)= A^k} (a)
(b) (b_{k) (b)}

I have some trouble to put the matrixs into the text, sorry

Thank you in advance for help:grin:

I don't understand. Is matrix A supposed to be a two by two matrix [A¹⁷ does not exist for A equal to a 1 row by 2 columns matrix as you have shown].

Write you matrix A as, for example,
1 0
0 1
for the 2x2 identity matrix
\(\displaystyle \begin{pmatrix}1& 0\\0& 1\end{pmatrix}\)
Write (1, 1, 1) for example for the row vector
\(\displaystyle \begin{pmatrix} 1& 1& 1\end{pmatrix}\)
or (1, 1, 1)^T for example for the column vector
\(\displaystyle \begin{pmatrix} 1\\1\\1\end{pmatrix}\)
The superscript T stands for transpose.

Of course you could use Latex (see a sample by doing a Reply With Quote). You could start with
ftp://ftp.ams.org/pub/tex/doc/amsmath/short-math-guide.pdf
for other examples. It also has more references.

 

[kikofra]

Sorry, i tried to put the matrix clear in the post, but with submition it become unclear.

I have a picture of the my exam where aperead the exercise:

now is more clear?

thank you