angela210793
  • angela210793
Inverting matrices :S
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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angela210793
  • angela210793
|dw:1328979083071:dw|
amistre64
  • amistre64
cofactor, transpose, divide by determinant
amistre64
  • amistre64
or swap some stuff in a 2x2

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angela210793
  • angela210793
let me try it and u tell me if i have solved it right ok???
anonymous
  • anonymous
yeah easy method for 2 by 2
amistre64
  • amistre64
forgot to transpose lol
amistre64
  • amistre64
last time .... and i forgot to use the checkerboard +- correctly a b c d cofactors to: d -c -b a transposes to d -c -b a then divide by determinate maybe!! lol
angela210793
  • angela210793
is this right? |dw:1328979427660:dw|
TuringTest
  • TuringTest
for invertible 2x2 matrices\[A=\left[\begin{matrix}a & b \\ c & d\end{matrix}\right]\]\[A^{-1}=\frac1{\det A}\left[\begin{matrix}d & -b \\ -c & a\end{matrix}\right]\]looks good angela
anonymous
  • anonymous
Trick: Swap the diagonal element and change the sign of off-diagonal ones
amistre64
  • amistre64
thats what i was trying for lol
angela210793
  • angela210793
I think cofactors will be d -b -c a
amistre64
  • amistre64
b is not its own cofactor
anonymous
  • anonymous
2 days back I learned a super fast way for doing 3x3 matrices
amistre64
  • amistre64
cofactor is the determinate of the submatrix
amistre64
  • amistre64
the submatrix of b is c in this case
angela210793
  • angela210793
Thanks guys :) How abt a 4x4 matrix????
anonymous
  • anonymous
\[ M = \left[ {\begin{array}{cc} x & y \\ z & w \\ \end{array} } \right] \] M = \begin{array}{cc} x & y \\ z & w \\ \end{array} \] \[ M^{-1}= \frac{1}{xw-yz}\left[ {\begin{array}{cc} w& -y \\ -z & x \\ \end{array} } \right] \]
anonymous
  • anonymous
For this one the answer is\[ \begin{bmatrix} \cos x & \sin x \\ -\sin x & \cos x \end{bmatrix} \]
amistre64
  • amistre64
same process just messier and more apt to computers
anonymous
  • anonymous
god it took me a long time to write that
angela210793
  • angela210793
well am not a computer....O.o
amistre64
  • amistre64
then youll have to get a monk
TuringTest
  • TuringTest
Cofactors is a good way to get bigger determinants if the matrix has some number of zeros in it
anonymous
  • anonymous
finding inverse of 4 by 4 by hand is long process, use a machine
anonymous
  • anonymous
I like to use reduce row-echelon for method for 4x4
anonymous
  • anonymous
i like to use maple
TuringTest
  • TuringTest
if it's like 0022 1536 0739 0297 you can expand the cofactors along the first column and you only need to take one determinant, all the minors are zero except for 1
angela210793
  • angela210793
ahhhhaaaa...I got it.....Thank you all ^^
amistre64
  • amistre64
a b c d e f g h i j k l m n o p +fgh - egh +efh -efg jkl ikl ijl ijk nop mop mnp mno etc ........... then transpose; and divide off the original determinate
angela210793
  • angela210793
Amistre u lost me....wht did u do in there??
amistre64
  • amistre64
the cofactor is the determinants of the submatrixes
amistre64
  • amistre64
its an algorithm
angela210793
  • angela210793
I'm sorry but all i know for algorithms is the name....I have no idea wht they r
amistre64
  • amistre64
|dw:1328980027433:dw|
angela210793
  • angela210793
i know wht submatrices r...
amistre64
  • amistre64
an algorithm is a means of operating on data multiplication is an algorithm; division is an algorithm its a process that aids us
amistre64
  • amistre64
it sorts the data into a usable form that we can maniipulate to our own devious devices :)
TuringTest
  • TuringTest
yeah, all that procedural stuff the process you use in long division for example computers do all problems with algorithms, they never think 'outside the box' so to speak
angela210793
  • angela210793
OMG!!! I'm going to fail :(
TuringTest
  • TuringTest
? why?
angela210793
  • angela210793
cause i have to colve 100 probs and i have solved only 10...yay :P
angela210793
  • angela210793
and my stupid teacher doesn't know to explain at all -_-
sasogeek
  • sasogeek
|dw:1328980182059:dw|
sasogeek
  • sasogeek
i know nothing about 4x4 matrices but i know there's something to do with + - + something somewhere dealing with cofactors and it should look something like this... not sure
sasogeek
  • sasogeek
i think that's what amistre did when he drew "a" and wrote "sub" in the box
TuringTest
  • TuringTest
that will get you the determinant of a 4x4 if you want the inverse I would probably use the row reduction thing
angela210793
  • angela210793
I kinda got it...
TuringTest
  • TuringTest
this is a good site http://tutorial.math.lamar.edu/Classes/LinAlg/FindingInverseMatrices.aspx
sasogeek
  • sasogeek
Angela, you need to get it, u don't need to "kinda" get it... that won't get u far lol :P
angela210793
  • angela210793
Leave me alone geek...:P I got microeconomy,finance,communication to study too -_-
sasogeek
  • sasogeek
welcome to university :)
angela210793
  • angela210793
yea right :'( I wish i never started it :P
Akshay_Budhkar
  • Akshay_Budhkar
i wish i start it soon! @angela
angela210793
  • angela210793
tht's cause u don't know yet wht it feels like to be in univ :p
Akshay_Budhkar
  • Akshay_Budhkar
if i dont go to univ i wont be great :P
angela210793
  • angela210793
u may go to univ and still not b great Akshay
Akshay_Budhkar
  • Akshay_Budhkar
i will be its a guarantee as it is "ME" :P
angela210793
  • angela210793
Ehe :P
Akshay_Budhkar
  • Akshay_Budhkar
u got matrices in economics?
angela210793
  • angela210793
yea we have maths...and we're getting too much information in just one lecture..teacher never shows an example to us and we're all like: ''Is tht chinese??''

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