Question

matrices help!

Answer 1

^ see attached

Answer 2

My thoughts were that if I can prove that R * R^t (its transpose) were equal to 1 then R^t = R^-1 (inverse)

Answer 3

R^T =[ 2/7 6/7 -3/7 ]
[6/7 3/7 2/7]
[3/7 2/7 6/7]

Answer 4

did you try to get the inverse?

Answer 5

wouldnt the first 6/7 on second row be neg?

Answer 6

I haven't tried to get the inverse yet.

Answer 7

yes negative im sorry my pc keeps hanging up on me lol

Answer 8

try to get the inverse

Answer 9

to get the inverse i have to find the determinant of the matrix and the transpose then i get a adjoint matrix then I divide the adjoint matrix by the determinant?

Answer 10

yes

Answer 11

k, brb have to try to do this on paper.

Answer 12

k

Answer 13

the answer would be the same as the R transpose

Answer 14

ffor the determinate R i got this

Answer 15

R^1= R adj / /R/

Answer 16

\[2/7(3/7*6/7-2/7*2/7)-6/7(-6/7*6/7-2/7*3/7)+-3/7(-6/7*2/7-3/7*3/7)\]

Answer 17

detR=/R/ = 1

Answer 18

is /R/ the adjoint of matrix? Sorry this stuff is pretty confusing to me

Answer 19

/R/ is the determinant of matrix R it is also det R=/A/

Answer 20

R adj= adjoint of R

Answer 21

okay. I tried to get the det R for the matrix above following http://analyzemath.com/Tutorial-System-Equations/determinants.html

Answer 22

which resulted in 1

Answer 23

like you said

Answer 24

ok thats good for the det R, now you can get the adjoint, try doing it

Answer 25

okay, brb, back to the note book haha

Answer 26

ok have fun lol

Answer 27

could you give me a little help, the books example on adjoint of the matrix is not very clear.

Answer 28

ok ill give you a good example hold on

Answer 29

okay, thanks again for the help

Answer 30

I think i may have gotten it, It came out the same as the tranpose matrix

Answer 31

if A=[ 1 2 3 ]
[ 0 4 5 ]
[ 1 0 6 ]
you need to find the cofactor of each

A11=[ 4 5 ] = 24 A12= -[ 0 5 ]
[ 0 6] [ 1 6 ] =5

A13 =[ 0 4 ]
[ 1 0 ] = -4
A21=-[ 2 3 ]
[ 0 6 ]= -12 etc....

then you will have cofactor of A= [ 24 5 -4]
[ -12 3 2]
[-2 -5 4]

then you can have adj A =[ 24 -12 -2 ]
[ 5 3 -5]
[ -4 2 4]

Answer 32

note here i use the co factor instead of the transpose

Answer 33

perfect I found a cofactor example too that help me along, thanks :)

Answer 34

yes the adj R is the same as transpose,,but they are not all the time equal....inthis case they are only equal

Answer 35

ok hope that help you out

Answer 36

perfect ! so i proved the second part! awesome thanks so much for your help

Answer 37

ok now have fun

Answer 38

yes, I guess my only other question is what did it mean by a proper rotation matrix?