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![[Post New]](/templates/default/images/icon_minipost_new.gif) 15 Feb 2008 12:15:04 IST
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*if A is skew symmetric matrix, then I-A is a. skew symmetric b. symmetric c. singular d. nonsingular I is identity matrix... *ABC r three matricesof the same order such that any 2 r symmetric and remainin 3rd is skew symmetric... now X= ABC +CBA and Y =ABC-CBA, thn (XY)T is a. symmetric b. skew symmetric c. -XY d. -YX plz. answer these givin complete ans. in ur own words AND PLZ. HELP ME IN SOLVING THESE TYPE OF PROB. WHAT IS TE WAY TO DO THIS.... do u have any article or any information regardin this that u thnk can help me then plz. bring it to my notice............ plz..........
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15 Feb 2008 12:53:15 IST
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1) skew symmetric again ....
because skew symmetric main diagonal acts as mirror and opposite elemnts have alternate signs... example
2 3 5
-3 2 4
-5 -4 2
now I identity matrix also has 1s along the diagonal.. so the diagonal's value decreases but other elements remain unchanged.... 1 0 0 2 3 5 0 1 0 - -3 2 4 0 0 1 -5 -4 2
= -1 -3 -5 3 -1 -4 5 4 -1
so it remains skew symmetric... though the signs on opposite sides of diagonal are inter changed and diagonal's value changes
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* Gaurav Ragtah ( aka Artemis Fowl )
* Agent 'G' [sniper] - SD-6 (Alliance of Twelve)
* Your friendly neighborhood spideyunlimited |
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15 Feb 2008 13:48:33 IST
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Q 1 : GIVEN A=-AT
(I-A)T=IT-AT=I+A
NOW, | I+A |2 =| I |2+|A|2+2|A||I| = 1+|A|2+2|A| =1 (since we know that for a skew symm matrix of odd order its determinant is zero)
so answer is non singular ...if it is not given that matrix is of odd order..then it will be zero only if det.A is =-1 so again it is nonsingular since it is not given that det.A is -1
* dont mind spidey but your answer seems to be wrong as in skew symm matrix diagnol elements shud be zero which are not coming in your case
Q 2 (XY)T=YTXT=(ABC-CBA)T(ABC+CBA)T=(ATBTCT-CTBTAT)(ATBTCT+CTBTAT)=(AB(-C)-(-C)BA)(AB(-C)+(-C)BA=(-ABC+CBA)(-ABC-CBA)=(ABC-CBA)(ABC+CBA)=YX=
now u can check if XandY commute each other then YX=XY or if they anti commute each other than YX=-XY
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15 Feb 2008 13:59:52 IST
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oh sorry i forgot that fact.
you're answer is correct then.
cheers!
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* Gaurav Ragtah ( aka Artemis Fowl )
* Agent 'G' [sniper] - SD-6 (Alliance of Twelve)
* Your friendly neighborhood spideyunlimited |
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15 Feb 2008 15:13:34 IST
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EDITED
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SAARE JAHAAN SE ACHCHA;
GOIIT HAMARA!!!!!!!!!!!!!!!!!!!!!!!!! |
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15 Feb 2008 15:16:00 IST
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EDITED
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SAARE JAHAAN SE ACHCHA;
GOIIT HAMARA!!!!!!!!!!!!!!!!!!!!!!!!! |
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15 Feb 2008 15:57:45 IST
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A=I is not a skew symmetric case.........first of all when A=I its elements in the diagonal will not be zero which is the required condition for skew symm matrix.......and about your first post, u have considered symm matrix but in question it is given that it is skew symm.......
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" The difficult we do immediately, impossible takes a little longer "
--- U.S. Army
"It's better to have a gun and not need it than to need a gun and
not have it."
--- The Sniper
"You can get more with a kind word and a gun than you can with a
kind word. "
--- The Sniper
"Join the Army: travel to exotic distant lands; meet exciting,
unusual people and kill them. "
--- The Sniper
"The victor will never be asked if he told the truth."
--- Adolf Hitler
"Stop talking, start doing"
--- IBM
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15 Feb 2008 16:10:23 IST
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ya sry dude, i too considered it to be symmetric like spidey ,
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15 Feb 2008 16:44:29 IST
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hey guys, thnx 4 da response but in 2nd prob. what sniper has done ... dont u thnk (ABC)^T = (C^T)(B^T)(A^T).... and so on..... and the ans. shud be only -XY.... but i cudnt understand by what does commute mean and how cud u get XY... plz. helpme... and in da first quest. a matrix is singular if its det. = 0, rit and why here it cant be singular? will det. of A never be equal to -1... and why do we rule out the symmetric option and see other 2 plz. see dis thnx
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15 Feb 2008 16:59:15 IST
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u r right i have done mistake......(ABC)T = CTBTAT only correct it
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" The difficult we do immediately, impossible takes a little longer "
--- U.S. Army
"It's better to have a gun and not need it than to need a gun and
not have it."
--- The Sniper
"You can get more with a kind word and a gun than you can with a
kind word. "
--- The Sniper
"Join the Army: travel to exotic distant lands; meet exciting,
unusual people and kill them. "
--- The Sniper
"The victor will never be asked if he told the truth."
--- Adolf Hitler
"Stop talking, start doing"
--- IBM
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15 Feb 2008 17:00:33 IST
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after correcting u need not worry about commute or anti commute u will straight away get -XY
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" The difficult we do immediately, impossible takes a little longer "
--- U.S. Army
"It's better to have a gun and not need it than to need a gun and
not have it."
--- The Sniper
"You can get more with a kind word and a gun than you can with a
kind word. "
--- The Sniper
"Join the Army: travel to exotic distant lands; meet exciting,
unusual people and kill them. "
--- The Sniper
"The victor will never be asked if he told the truth."
--- Adolf Hitler
"Stop talking, start doing"
--- IBM
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Q 2 (XY)T=YTXT=(ABC-CBA)T(ABC+CBA)T=(CTBTAT-ATBTCT)(CTBTAT+ATBTCT)=((-C)BA-AB(-C))((-C)BA+AB(-C))=(-CBA+ABC)(-CBA-ABC)
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" The difficult we do immediately, impossible takes a little longer "
--- U.S. Army
"It's better to have a gun and not need it than to need a gun and
not have it."
--- The Sniper
"You can get more with a kind word and a gun than you can with a
kind word. "
--- The Sniper
"Join the Army: travel to exotic distant lands; meet exciting,
unusual people and kill them. "
--- The Sniper
"The victor will never be asked if he told the truth."
--- Adolf Hitler
"Stop talking, start doing"
--- IBM
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15 Feb 2008 17:08:17 IST
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yes thnx thts what i was thnkin and what abt. the other prob. and sniper what is this commute and anti commute?
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15 Feb 2008 17:10:10 IST
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WHEN AB=BA THIS MEANS A AND B COMMUTE EACH OTHER
WHEN AB=-BA THIS MEANS A AND B ANTI COMMUTE EACH OTHER
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" The difficult we do immediately, impossible takes a little longer "
--- U.S. Army
"It's better to have a gun and not need it than to need a gun and
not have it."
--- The Sniper
"You can get more with a kind word and a gun than you can with a
kind word. "
--- The Sniper
"Join the Army: travel to exotic distant lands; meet exciting,
unusual people and kill them. "
--- The Sniper
"The victor will never be asked if he told the truth."
--- Adolf Hitler
"Stop talking, start doing"
--- IBM
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