Inverting matrices :S

- angela210793

Inverting matrices :S

- katieb

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- angela210793

|dw:1328979083071:dw|

- amistre64

cofactor, transpose, divide by determinant

- amistre64

or swap some stuff in a 2x2

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## More answers

- angela210793

let me try it and u tell me if i have solved it right ok???

- anonymous

yeah easy method for 2 by 2

- amistre64

forgot to transpose lol

- 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

is this right? |dw:1328979427660:dw|

- 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

Trick: Swap the diagonal element and change the sign of off-diagonal ones

- amistre64

thats what i was trying for lol

- angela210793

I think cofactors will be
d -b
-c a

- amistre64

b is not its own cofactor

- anonymous

2 days back I learned a super fast way for doing 3x3 matrices

- amistre64

cofactor is the determinate of the submatrix

- amistre64

the submatrix of b is c in this case

- angela210793

Thanks guys :)
How abt a 4x4 matrix????

- 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

For this one the answer is\[ \begin{bmatrix}
\cos x & \sin x \\
-\sin x & \cos x
\end{bmatrix} \]

- amistre64

same process just messier and more apt to computers

- anonymous

god it took me a long time to write that

- angela210793

well am not a computer....O.o

- amistre64

then youll have to get a monk

- TuringTest

Cofactors is a good way to get bigger determinants if the matrix has some number of zeros in it

- anonymous

finding inverse of 4 by 4 by hand is long process, use a machine

- anonymous

I like to use reduce row-echelon for method for 4x4

- anonymous

i like to use maple

- 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

ahhhhaaaa...I got it.....Thank you all ^^

- 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

Amistre u lost me....wht did u do in there??

- amistre64

the cofactor is the determinants of the submatrixes

- amistre64

its an algorithm

- angela210793

I'm sorry but all i know for algorithms is the name....I have no idea wht they r

- amistre64

|dw:1328980027433:dw|

- angela210793

i know wht submatrices r...

- 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

it sorts the data into a usable form that we can maniipulate to our own devious devices :)

- 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

OMG!!! I'm going to fail :(

- TuringTest

? why?

- angela210793

cause i have to colve 100 probs and i have solved only 10...yay :P

- angela210793

and my stupid teacher doesn't know to explain at all -_-

- sasogeek

|dw:1328980182059:dw|

- 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

i think that's what amistre did when he drew "a" and wrote "sub" in the box

- TuringTest

that will get you the determinant of a 4x4
if you want the inverse I would probably use the row reduction thing

- angela210793

I kinda got it...

- TuringTest

this is a good site
http://tutorial.math.lamar.edu/Classes/LinAlg/FindingInverseMatrices.aspx

- sasogeek

Angela, you need to get it, u don't need to "kinda" get it... that won't get u far lol :P

- angela210793

Leave me alone geek...:P I got microeconomy,finance,communication to study too -_-

- sasogeek

welcome to university :)

- angela210793

yea right :'( I wish i never started it :P

- Akshay_Budhkar

i wish i start it soon! @angela

- angela210793

tht's cause u don't know yet wht it feels like to be in univ :p

- Akshay_Budhkar

if i dont go to univ i wont be great :P

- angela210793

u may go to univ and still not b great Akshay

- Akshay_Budhkar

i will be its a guarantee as it is "ME" :P

- angela210793

Ehe :P

- Akshay_Budhkar

u got matrices in economics?

- 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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