## angela210793 3 years ago Inverting matrices :S

1. angela210793

|dw:1328979083071:dw|

2. amistre64

cofactor, transpose, divide by determinant

3. amistre64

or swap some stuff in a 2x2

4. angela210793

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

5. satellite73

yeah easy method for 2 by 2

6. amistre64

forgot to transpose lol

7. 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

8. angela210793

is this right? |dw:1328979427660:dw|

9. 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

10. FoolForMath

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

11. amistre64

thats what i was trying for lol

12. angela210793

I think cofactors will be d -b -c a

13. amistre64

b is not its own cofactor

14. FoolForMath

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

15. amistre64

cofactor is the determinate of the submatrix

16. amistre64

the submatrix of b is c in this case

17. angela210793

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

18. satellite73

$M = \left[ {\begin{array}{cc} x & y \\ z & w \\ \end{array} } \right]$ M = \begin{array}{cc} x & y \\ z & w \\ \end{array} \] $M^{-1}= \frac{1}{xw-yz}\left[ {\begin{array}{cc} w& -y \\ -z & x \\ \end{array} } \right]$

19. FoolForMath

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

20. amistre64

same process just messier and more apt to computers

21. satellite73

god it took me a long time to write that

22. angela210793

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

23. amistre64

then youll have to get a monk

24. TuringTest

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

25. satellite73

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

26. FoolForMath

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

27. satellite73

i like to use maple

28. 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

29. angela210793

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

30. 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

31. angela210793

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

32. amistre64

the cofactor is the determinants of the submatrixes

33. amistre64

its an algorithm

34. angela210793

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

35. amistre64

|dw:1328980027433:dw|

36. angela210793

i know wht submatrices r...

37. amistre64

an algorithm is a means of operating on data multiplication is an algorithm; division is an algorithm its a process that aids us

38. amistre64

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

39. 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

40. angela210793

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

41. TuringTest

? why?

42. angela210793

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

43. angela210793

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

44. sasogeek

|dw:1328980182059:dw|

45. 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

46. sasogeek

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

47. TuringTest

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

48. angela210793

I kinda got it...

49. TuringTest

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

50. sasogeek

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

51. angela210793

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

52. sasogeek

welcome to university :)

53. angela210793

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

54. Akshay_Budhkar

i wish i start it soon! @angela

55. angela210793

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

56. Akshay_Budhkar

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

57. angela210793

u may go to univ and still not b great Akshay

58. Akshay_Budhkar

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

59. angela210793

Ehe :P

60. Akshay_Budhkar

u got matrices in economics?

61. 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??''