Matrix Number and Solving Equation.

[lvl107]

Hello Everyone,

I have a question, wish learning, and really need help. It's about "Matrix Number and Solving Equation."

solve,X.

Thanks in advance for the time and help.

Best regards,

Loi Le.

[AlanStevens · Accepted solution]

Do you mean like so?

Alan

[RichardJ]

Why column by column? Why not just X=M^-1*C?

[AlanStevens]

Richard Jackson wrote:

Why column by column? Why not just X=M^-1*C?

Why not indeed!! That works too!

Alan

[lvl107]

Many, many thanks, Alan. I think I am a new with "matrix". And I have comprehended your suggestion as the following :

Thanks again.

Best regards,

Loi.

[lvl107]

Oh, It seems could be the following :

[RichardJ]

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.

[MikeArmstrong]

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

[RichardJ]

How do you divide one matrix by another?

[MikeArmstrong]

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

[StuartBruff]

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.

[lvl107]

Thank to all who replied.

Best regards,

Loi.

[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.

[AlanStevens]

Loi Le wrote:

Hello Everyone again,

I still have a related question:

solve,X

Thanks in advance for the time and help, again.

Best regards,

Loi Le.

This is, in effect, trying to find four unknowns with three equations!

Alan

[lvl107]

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.

[AlanStevens]

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?

[lvl107]

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

[lvl107]

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.

[AlanStevens]

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

[AlanStevens]

The attached shows a more direct way of finding the solution to such equations.

Alan

[lvl107]

Many, many thanks, Alan. I prefer "direct way" such that.

Thanks again.

Best regards,

Loi.

[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