| |
 |
|
|
Science Forum Index » Math - Symbolic Forum » Matrices problem
Page 1 of 1
|
| Author |
Message |
| sina1260 |
 Posted: Sun Jun 03, 2007 5:45 pm |
|
|
|
Guest
|
hello, i have this project that i have to do and i need help to solve
it.
1. Consider matrix M= [2 0 , 0 2] calculate M^n for n= 2, 3, 4, 5, 10,
20, 50. Describe in words any pattern observed. Use this pattern to
find a general expression for matrix M^n in terms of n
2. Consider matrices P=[3 1, 1 3] and S= [4 2, 2 4]
P^2=[3 1, 1 3]^2 =[10 6, 6 10]=2[5 3, 3 5]
S^2= [3 1, 1 3]^2=[20 16, 16 20]=2[10 8, 8 10]
Calculate P^n and S^n for other values of n and describe any
pattern(s) you obesrve.
3. Consider [k+1 k-1, k-1 k+1]
Steps 1 and 2 contain examples of these matrices for k=1, 2, and 3.
Consider other values of k and describe any pattern(s) you observe.
Generalize these results in terms of k and n
4. Use technology (calculator and computer) to investigate what
happens when further values of k & n. State scope of limitations
of k and n.
5.Explain why your results hold true in general.
-------------= Posted from Ugroups.com =-------------
---= Fast & Free Web Portal to Usenet Newsgroups =---
-------------= http://www.ugroups.com/ =------------- |
|
|
| Back to top |
|
| rjf |
| Posted: Mon Jun 04, 2007 7:18 am |
|
|
|
Guest
|
On Jun 3, 3:45 pm, sina_1...@yahoo-dot-com.no-spam.invalid (sina1260)
wrote:
Quote: hello, i have this project that i have to do and i need help to solve
it.
Wrong newsgroup. You want the "please do my homework" newsgroup.
Reaally, if you have problems with your homework, why not ask your
instructor? |
|
|
| Back to top |
|
| sina1260 |
| Posted: Mon Jun 04, 2007 3:45 pm |
|
|
|
Guest
|
thats because he said that we have to do this by ourselfs.
thanks for the info but where is that exactly? i'm new here.
-------------= Posted from Ugroups.com =-------------
---= Fast & Free Web Portal to Usenet Newsgroups =---
-------------= http://www.ugroups.com/ =------------- |
|
|
| Back to top |
|
| Robert Israel |
| Posted: Mon Jun 04, 2007 7:15 pm |
|
|
|
Guest
|
|
| Back to top |
|
| Jeremy Watts |
| Posted: Tue Jun 05, 2007 5:16 am |
|
|
|
Guest
|
"sina1260" <sina_1260@yahoo-dot-com.no-spam.invalid> wrote in message
news:1180910736_34091@sp6iad.superfeed.net...
Quote: hello, i have this project that i have to do and i need help to solve
it.
1. Consider matrix M= [2 0 , 0 2] calculate M^n for n= 2, 3, 4, 5, 10,
20, 50. Describe in words any pattern observed. Use this pattern to
find a general expression for matrix M^n in terms of n
how are you meant to calculate M^n for a non-square matrix?
Quote:
2. Consider matrices P=[3 1, 1 3] and S= [4 2, 2 4]
P^2=[3 1, 1 3]^2 =[10 6, 6 10]=2[5 3, 3 5]
S^2= [3 1, 1 3]^2=[20 16, 16 20]=2[10 8, 8 10]
Calculate P^n and S^n for other values of n and describe any
pattern(s) you obesrve.
3. Consider [k+1 k-1, k-1 k+1]
Steps 1 and 2 contain examples of these matrices for k=1, 2, and 3.
Consider other values of k and describe any pattern(s) you observe.
Generalize these results in terms of k and n
4. Use technology (calculator and computer) to investigate what
happens when further values of k & n. State scope of limitations
of k and n.
5.Explain why your results hold true in general.
-------------= Posted from Ugroups.com =-------------
---= Fast & Free Web Portal to Usenet Newsgroups =---
-------------= http://www.ugroups.com/ =-------------
|
|
|
| Back to top |
|
| Jeremy Watts |
| Posted: Tue Jun 05, 2007 5:23 am |
|
|
|
Guest
|
"Jeremy Watts" <jwatts1970@hotmail.com> wrote in message
news:JJa9i.6298$E9.1057@newsfe6-gui.ntli.net...
Quote:
"sina1260" <sina_1260@yahoo-dot-com.no-spam.invalid> wrote in message
news:1180910736_34091@sp6iad.superfeed.net...
hello, i have this project that i have to do and i need help to solve
it.
1. Consider matrix M= [2 0 , 0 2] calculate M^n for n= 2, 3, 4, 5, 10,
20, 50. Describe in words any pattern observed. Use this pattern to
find a general expression for matrix M^n in terms of n
how are you meant to calculate M^n for a non-square matrix?
or is M meant to be :-
2 0
M = 0 2
Quote:
2. Consider matrices P=[3 1, 1 3] and S= [4 2, 2 4]
P^2=[3 1, 1 3]^2 =[10 6, 6 10]=2[5 3, 3 5]
S^2= [3 1, 1 3]^2=[20 16, 16 20]=2[10 8, 8 10]
Calculate P^n and S^n for other values of n and describe any
pattern(s) you obesrve.
3. Consider [k+1 k-1, k-1 k+1]
Steps 1 and 2 contain examples of these matrices for k=1, 2, and 3.
Consider other values of k and describe any pattern(s) you observe.
Generalize these results in terms of k and n
4. Use technology (calculator and computer) to investigate what
happens when further values of k & n. State scope of limitations
of k and n.
5.Explain why your results hold true in general.
-------------= Posted from Ugroups.com =-------------
---= Fast & Free Web Portal to Usenet Newsgroups =---
-------------= http://www.ugroups.com/ =-------------
|
|
|
| Back to top |
|
| sina1260 |
| Posted: Tue Jun 05, 2007 8:50 am |
|
|
|
Guest
|
M is {2 0}
{0 2}
-------------= Posted from Ugroups.com =-------------
---= Fast & Free Web Portal to Usenet Newsgroups =---
-------------= http://www.ugroups.com/ =------------- |
|
|
| Back to top |
|
| Jeremy Watts |
| Posted: Tue Jun 05, 2007 1:01 pm |
|
|
|
Guest
|
"sina1260" <sina_1260@yahoo-dot-com.no-spam.invalid> wrote in message
news:1181051432_38173@sp6iad.superfeed.net...
how have you been shown how to find powers of matrices? if you know that :-
M^2 = M * M
then how would you find M^4 more easily than by saying :-
M^4 = M * M * M * M ??
remembering that, M^4 = (M^2) ^2
knowing this then, how would you find M^8 say?
Quote:
-------------= Posted from Ugroups.com =-------------
---= Fast & Free Web Portal to Usenet Newsgroups =---
-------------= http://www.ugroups.com/ =-------------
|
|
|
| Back to top |
|
| |
|
Page 1 of 1
All times are GMT - 5 Hours
The time now is Wed Jan 07, 2009 1:21 pm
|
|