
Re: Matrix Number and Solving Equation.
AlanStevens Mar 15, 2011 11:33 AM (in response to lvl107)Do you mean like so?
Alan

Re: Matrix Number and Solving Equation.
A.Non Mar 15, 2011 11:36 AM (in response to AlanStevens)Why column by column? Why not just X=M^1*C?

Re: Matrix Number and Solving Equation.
AlanStevens Mar 15, 2011 12:01 PM (in response to A.Non)Richard Jackson wrote:
Why column by column? Why not just X=M^1*C?
Why not indeed!! That works too!
Alan


Re: Matrix Number and Solving Equation.
lvl107 Mar 15, 2011 3:05 PM (in response to AlanStevens)Many, many thanks, Alan. I think I am a new with "matrix". And I have comprehended your suggestion as the following :
Best regards,
Loi.



Re: Matrix Number and Solving Equation.
A.Non Mar 15, 2011 11:34 AM (in response to lvl107)You solve it much the same way that you solve a simple algebraic equation. The basic rule is that you can perform a manipulation on the left hand side of the equaiotn as long as you perform the same manipulation on the right hand side. The main thing to be aware of is that matrix mulitplication is generally not commutative (i.e. A*B is not equal to B*A). This means there is a distinction between premultiplication and postmultiplication.
If you premultiply the first matrix on the left hand side by it's inverse you get the identity matrix, which is the matrix equivalent of 1. That leaves you, in effect, with only X on the left. So you must also premultiply the matrix on the right hand side by the same matrix (i.e. the inverse of the first matrix on the left hand side). The result is your solution.

Re: Matrix Number and Solving Equation.
MikeArmstrong Mar 15, 2011 11:53 AM (in response to A.Non)You solve it much the same way that you solve a simple algebraic equation. The basic rule is that you can perform a manipulation on the left hand side of the equaiotn as long as you perform the same manipulation on the right hand side.
I am being stupid here???
It doesn't have to be multiplication does it. Couldn't the left hand side of the equation be divided by the left hand side matrix to leave X and then do the same on the right hand said?
Mike

Re: Matrix Number and Solving Equation.
A.Non Mar 15, 2011 11:58 AM (in response to MikeArmstrong)How do you divide one matrix by another?

Re: Matrix Number and Solving Equation.
MikeArmstrong Mar 15, 2011 1:48 PM (in response to A.Non)How do you divide one matrix by another?
Sorry you can't.
As you said, In higher math you generalize the notion of division to that of multiplication by the inverse.
Mike

Re: Matrix Number and Solving Equation.
StuartBruff Mar 15, 2011 4:11 PM (in response to A.Non)Richard Jackson wrote:
How do you divide one matrix by another?
Diagonalize the first matrix, remove the upper zeros, rotate it through π/8 and then ram it hard into the bottom row of the other matrix. Do it right and that old matrix just splits in two. Works for me.




Re: Matrix Number and Solving Equation.
lvl107 Mar 15, 2011 3:11 PM (in response to lvl107)Thank to all who replied.
Best regards,
Loi.

Re: Matrix Number and Solving Equation.
lvl107 Mar 15, 2011 6:37 PM (in response to lvl107)Hello Everyone again,
I still have a related question:
solve,X
Thanks in advance for the time and help, again.
Best regards,
Loi Le.


Re: Matrix Number and Solving Equation.
lvl107 Mar 16, 2011 6:15 AM (in response to AlanStevens)I think I am a new with "matrix multiplication". As Richard said above : "matrix multiplication is generally not commutative". I have forgot that. But I still have a query : "Could the following equation be solved ?" :
solve,X.
I am very interested in that. Thanks in advance for the time and help.
Best regards,
Loi Le.

Re: Matrix Number and Solving Equation.
AlanStevens Mar 17, 2011 4:19 AM (in response to lvl107)Like so?
Alan
NB You should note that each row of three components of X is defined by four equations!! So what does that tell you?

MatrixEqn.mcd.zip 6.8 K

Re: Matrix Number and Solving Equation.
lvl107 Mar 17, 2011 7:05 PM (in response to AlanStevens)I got it. I greatly appreciate your answer to my extra question, Alan. That is the thing I was very interested in.
Thanks again.
Best regards,
Loi.
Message was edited by: Loi Le

Re: Matrix Number and Solving Equation.
lvl107 Mar 21, 2011 1:40 PM (in response to AlanStevens)Alan,
Following up your suggestion above, I still have a very small query : "tidy it up issue" (for checking root).
solve,X.
Attach File below.
Regards,
Loi.

Re: Matrix Number and Solving Equation.
AlanStevens Mar 22, 2011 2:12 AM (in response to lvl107)Loi Le wrote:
Alan,
Following up your suggestion above, I still have a very small query : "tidy it up issue" (for checking root).
solve,X.
Attach File below.
Regards,
Loi.
See attached.
Alan

Re: Matrix Number and Solving Equation.
AlanStevens Mar 22, 2011 3:40 AM (in response to lvl107)The attached shows a more direct way of finding the solution to such equations.
Alan






Re: Matrix Number and Solving Equation.
lvl107 Mar 17, 2011 6:24 PM (in response to lvl107)Hello Everyone again,
Going through the above, with intuition, I was wondering whether could a matrix was factorize into matrices factor. (multiplication of matrices).
factorize,C
Thanks in advance for the time and help.
Best regards,
Loi Le.
Message was edited by: Loi Le
