Question

matrix multiplication

Answer 1

comp being slow, pls wait..

Answer 2

ok what is the matrix problem

Answer 3

let x be an arbitrary angle and C represents cosine, S represent Sine

Answer 4

and what are the dimensions of those matrices

Answer 5

matrix A=
CX -SX 0 aCX
SX CX 0 aSX
0 0 1 0
0 0 0 1

matrix B=
CY -SY 0 bCY
SY CY 0 bSY
0 0 1 0
0 0 0 1

Answer 6

and Y another arbitrary angle..

Answer 7

4x4 matrix

Answer 8

i think i get how to do the multiplication but since there are variables, i'm coming up with crazy figures for each new element in the new matrix. and this new matrix has to be multiplied by another 4x4

Answer 9

ok

Answer 10

i guess my problem is more towards trig...is there a simple expressions for each element?

Answer 11

i will solve for u as soon as i am done with the other student

Answer 12

thx, or you can just tell me if there's no simple expression cuz i can do all the work, it will just look messy

Answer 13

4x4 is a messy matrix, so should expect such a mess

Answer 14

ok. or are you familiar with matlab? from what i remember, you have to have values for matlab...

Answer 15

do u want to do this with matlab or using normal mathematical methods

Answer 16

it's just part of the actual problem so i don't think working it out by hand is important so if i can do it on matlab, it would be great

Answer 17

or calculator

Answer 18

ok i will do it for u with c++ or c sharp

Answer 19

so u just want to multiply those two matrices

Answer 20

i'm not familiar with c++ but there is another matrix, i will type it up..

Answer 21

Matrix C=
CZ -SZ 0 cCZ
SZ CZ 0 cSZ
0 0 1 0
0 0 0 1

Answer 22

and a,b,c are arbitrary constants. so in c++, you can keep the expression with variables?

Answer 23

do u want AxBxC

Answer 24

if that means the same thing as
AxB=AB
ABxC=result 4x4 matrix

Answer 25

ok

Answer 26

no it does not mean the same thing but i get what u want now

Answer 27

ok thx

Answer 28

am sorry of the delay just someone before u sent me a bunch of questions that i need to type the answers

Answer 29

so u can do others stuff and i will finish the work for u as soon as possible

Answer 30

that's fine, i will check later

Answer 31

sorry for keeping u waiting but i need to know do u want element by element multiplication or linear algebraic product

Answer 32

you have to be precise on that so i can give u the right answer

Answer 33

good question, i was actually trying to figure out on google. all the instructor said was to multiply them. what i found on google was this http://easycalculation.com/matrix/learn-matrix-multiplication.php which is what's going to make the result matrix look real messy. the problem is to find the transformation matrix of a mechanical grabber. so it would have multiple joints, point O as fixed, and point P as the position of the grabber. to find the position, find transformation matrices (which i've done) and the post multipy the matrices to get the result matrix. the matrix C was from point O to joint 1, matrix B is from joint 1 to joint 2, and matrix A is from joint 2 to point P

Answer 34

HI THERE I KNOW IT TOOK ME A LONG TIME BUT I PROMISED SOMEONE TO FINISH THERE 50 QUESTIONS

Answer 35

syms cosx sinx asinx acosx cosy siny bcosy bsiny cosz sinz csinz ccosz
syms cosx sinx asinx acosx cosy siny bcosy bsiny cosz sinz csinz ccosz


A=[cosx, -sinx,0, acosx;sinx,cosx,0,asinx;0,0,1,0;0,0,0,1];
B=[cosy, -siny,0, bcosy;siny,cosy,0,bsiny;0,0,1,0;0,0,0,1];
%C=[cosz, -sinz,0, ccosz;sinz,cosz,0,csinz;0,0,1,0;0,0,0,1];

%Linear algebraic product of the matrices...
M1= A * B * C;
M2= A*B;
M3= B*C;
M4= A*C;

%Array arithmetic operations are carried out element by element

M1= A * B * C;
M2= A*B;
M3= B*C;
M4= A*C;

Answer 36

the result for linear algebraic multiplication for example
A x B

Answer 37

A =

[ cosx, -sinx, 0, acosx]
[ sinx, cosx, 0, asinx]
[ 0, 0, 1, 0]
[ 0, 0, 0, 1]

Answer 38

B =

[ cosy, -siny, 0, bcosy]
[ siny, cosy, 0, bsiny]
[ 0, 0, 1, 0]
[ 0, 0, 0, 1]

Answer 39

A*B

ans =

[ cosx*cosy - sinx*siny, - cosx*siny - cosy*sinx, 0, acosx + bcosy*cosx - bsiny*sinx]
[ cosx*siny + cosy*sinx, cosx*cosy - sinx*siny, 0, asinx + bsiny*cosx + bcosy*sinx]
[ 0, 0, 1, 0]
[ 0, 0, 0, 1]

Answer 40

so this is what u called messy result which seems to be exclusive of your intuitive expectation, however the element by element matrix multiplication would give a result hopefully to your expectation

Answer 41

A.*B

ans =

[ cosx*cosy, sinx*siny, 0, acosx*bcosy]
[ sinx*siny, cosx*cosy, 0, asinx*bsiny]
[ 0, 0, 1, 0]
[ 0, 0, 0, 1]

Answer 42

Array arithmetic operations are carried out element by element, and can be used with multidimensional arrays. The period character (.) distinguishes the array operations from the matrix operations.

Answer 43

Sorry i was busy but i have to keep all my promises not matter what, so all the best and good luck.

Answer 44

Now with this basic method you can do whatever multiplication you want, and in any associative, distributive ... way you want.

Answer 45

thank you, i think i will have to ask which multiplication is needed since i don't know. i would hope it's the easier one though!