angela210793
Inverting matrices :S
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angela210793
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|dw:1328979083071:dw|
amistre64
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cofactor, transpose, divide by determinant
amistre64
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or swap some stuff in a 2x2
angela210793
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let me try it and u tell me if i have solved it right ok???
anonymous
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yeah easy method for 2 by 2
amistre64
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forgot to transpose lol
amistre64
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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
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is this right? |dw:1328979427660:dw|
TuringTest
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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
FoolForMath
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Trick: Swap the diagonal element and change the sign of off-diagonal ones
amistre64
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thats what i was trying for lol
angela210793
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I think cofactors will be
d -b
-c a
amistre64
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b is not its own cofactor
FoolForMath
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2 days back I learned a super fast way for doing 3x3 matrices
amistre64
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cofactor is the determinate of the submatrix
amistre64
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the submatrix of b is c in this case
angela210793
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Thanks guys :)
How abt a 4x4 matrix????
anonymous
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\[
M =
\left[ {\begin{array}{cc}
x & y \\
z & w \\
\end{array} } \right]
\]
M =
\begin{array}{cc}
x & y \\
z & w \\
\end{array}
\]
\[
M^{-1}=
\frac{1}{xw-yz}\left[ {\begin{array}{cc}
w& -y \\
-z & x \\
\end{array} } \right]
\]
FoolForMath
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For this one the answer is\[ \begin{bmatrix}
\cos x & \sin x \\
-\sin x & \cos x
\end{bmatrix} \]
amistre64
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same process just messier and more apt to computers
anonymous
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god it took me a long time to write that
angela210793
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well am not a computer....O.o
amistre64
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then youll have to get a monk
TuringTest
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Cofactors is a good way to get bigger determinants if the matrix has some number of zeros in it
anonymous
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finding inverse of 4 by 4 by hand is long process, use a machine
FoolForMath
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I like to use reduce row-echelon for method for 4x4
anonymous
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i like to use maple
TuringTest
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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
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ahhhhaaaa...I got it.....Thank you all ^^
amistre64
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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
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Amistre u lost me....wht did u do in there??
amistre64
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the cofactor is the determinants of the submatrixes
amistre64
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its an algorithm
angela210793
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I'm sorry but all i know for algorithms is the name....I have no idea wht they r
amistre64
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|dw:1328980027433:dw|
angela210793
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i know wht submatrices r...
amistre64
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an algorithm is a means of operating on data
multiplication is an algorithm; division is an algorithm
its a process that aids us
amistre64
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it sorts the data into a usable form that we can maniipulate to our own devious devices :)
TuringTest
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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
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OMG!!! I'm going to fail :(
TuringTest
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? why?
angela210793
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cause i have to colve 100 probs and i have solved only 10...yay :P
angela210793
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and my stupid teacher doesn't know to explain at all -_-
sasogeek
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|dw:1328980182059:dw|
sasogeek
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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
sasogeek
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i think that's what amistre did when he drew "a" and wrote "sub" in the box
TuringTest
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that will get you the determinant of a 4x4
if you want the inverse I would probably use the row reduction thing
angela210793
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I kinda got it...
sasogeek
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Angela, you need to get it, u don't need to "kinda" get it... that won't get u far lol :P
angela210793
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Leave me alone geek...:P I got microeconomy,finance,communication to study too -_-
sasogeek
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welcome to university :)
angela210793
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yea right :'( I wish i never started it :P
Akshay_Budhkar
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i wish i start it soon! @angela
angela210793
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tht's cause u don't know yet wht it feels like to be in univ :p
Akshay_Budhkar
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if i dont go to univ i wont be great :P
angela210793
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u may go to univ and still not b great Akshay
Akshay_Budhkar
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i will be its a guarantee as it is "ME" :P
angela210793
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Ehe :P
Akshay_Budhkar
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u got matrices in economics?
angela210793
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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??''