Inverting matrices :S

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|dw:1328979083071:dw|
cofactor, transpose, divide by determinant
or swap some stuff in a 2x2

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let me try it and u tell me if i have solved it right ok???
yeah easy method for 2 by 2
forgot to transpose lol
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
is this right? |dw:1328979427660:dw|
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
Trick: Swap the diagonal element and change the sign of off-diagonal ones
thats what i was trying for lol
I think cofactors will be d -b -c a
b is not its own cofactor
2 days back I learned a super fast way for doing 3x3 matrices
cofactor is the determinate of the submatrix
the submatrix of b is c in this case
Thanks guys :) How abt a 4x4 matrix????
\[ M = \left[ {\begin{array}{cc} x & y \\ z & w \\ \end{array} } \right] \] M = \begin{array}{cc} x & y \\ z & w \\ \end{array} \] \[ M^{-1}= \frac{1}{xw-yz}\left[ {\begin{array}{cc} w& -y \\ -z & x \\ \end{array} } \right] \]
For this one the answer is\[ \begin{bmatrix} \cos x & \sin x \\ -\sin x & \cos x \end{bmatrix} \]
same process just messier and more apt to computers
god it took me a long time to write that
well am not a computer....O.o
then youll have to get a monk
Cofactors is a good way to get bigger determinants if the matrix has some number of zeros in it
finding inverse of 4 by 4 by hand is long process, use a machine
I like to use reduce row-echelon for method for 4x4
i like to use maple
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
ahhhhaaaa...I got it.....Thank you all ^^
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
Amistre u lost me....wht did u do in there??
the cofactor is the determinants of the submatrixes
its an algorithm
I'm sorry but all i know for algorithms is the name....I have no idea wht they r
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i know wht submatrices r...
an algorithm is a means of operating on data multiplication is an algorithm; division is an algorithm its a process that aids us
it sorts the data into a usable form that we can maniipulate to our own devious devices :)
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
OMG!!! I'm going to fail :(
? why?
cause i have to colve 100 probs and i have solved only 10...yay :P
and my stupid teacher doesn't know to explain at all -_-
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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
i think that's what amistre did when he drew "a" and wrote "sub" in the box
that will get you the determinant of a 4x4 if you want the inverse I would probably use the row reduction thing
I kinda got it...
this is a good site http://tutorial.math.lamar.edu/Classes/LinAlg/FindingInverseMatrices.aspx
Angela, you need to get it, u don't need to "kinda" get it... that won't get u far lol :P
Leave me alone geek...:P I got microeconomy,finance,communication to study too -_-
welcome to university :)
yea right :'( I wish i never started it :P
i wish i start it soon! @angela
tht's cause u don't know yet wht it feels like to be in univ :p
if i dont go to univ i wont be great :P
u may go to univ and still not b great Akshay
i will be its a guarantee as it is "ME" :P
Ehe :P
u got matrices in economics?
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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