Master Matrices: Converting 5x5 to 4x4 with Ease for Your Coursework

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SamMcCrae
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How can I turn a 5x5 matrix into a 4x4? I really cannot remember and I need to do it in a coursework I am doing :/ I have a handout on how to do 4x4 into 3x3 but the handout is very confusing.
 

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How can I turn a 5x5 matrix into a 4x4?

Do you mean find the determinant of a 5x5 matrix by expanding it to 4x4 then 3x3 etc?
 
Studiot said:
Do you mean find the determinant of a 5x5 matrix by expanding it to 4x4 then 3x3 etc?
Well I don't quite want the determinant yet, I want to make it into a 4x4 now so I can see that it matches up with another 4x4 I've created by a different method (Well that's what I'm ment to do). But I will want the determinant eventually :P
 
micromass said:
Do you mean that you're given a 5x5-matrix and a 4x4-matrix and you want to find out whether they have the same determinant?? Is that what you want to solve?

I have a 4x4, and a 5x5, I want to make the 5x5 into a 4x4 so that they are both 4x4 and I can verify that they are the same. Determinant will be done later.
 
SamMcCrae said:
I have a 4x4, and a 5x5, I want to make the 5x5 into a 4x4 so that they are both 4x4 and I can verify that they are the same. Determinant will be done later.

I'm sorry but this makes no sense. What do you mean with "make a 5x5 into a 4x4"??

How can a 5x5-matrix be the same as a 4x4-matrix?? They are not the same by definition.

Can you give an example of what exactly you mean??
 
micromass said:
I'm sorry but this makes no sense. What do you mean with "make a 5x5 into a 4x4"??

How can a 5x5-matrix be the same as a 4x4-matrix?? They are not the same by definition.

Can you give an example of what exactly you mean??

I was given a method of how to turn a 4x4 into a 3x3 so it is easy to solve which involves moving stuff about and multiplying things. I'll go take a picture of the notes in a minute. We have all to turn a 5x5 into an equivalent 4x4 but I don't totally understand how to.
 
SamMcCrae said:
I was given a method of how to turn a 4x4 into a 3x3 so it is easy to solve which involves moving stuff about and multiplying things. I'll go take a picture of the notes in a minute. We have all to turn a 5x5 into an equivalent 4x4 but I don't totally understand how to.

I think you've misunderstood either what you're doing or what the question is asking for. You don't "solve" a matrix; a matrix just represents a transformation. You can "solve" an equation for the determinant of a matrix through cofactor expansion, which might be what you're talking about. You can't "turn a 5x5 matrix into a 4x4 matrix"; they don't even operate on the same sets.
 
Number Nine said:
I think you've misunderstood either what you're doing or what the question is asking for. You don't "solve" a matrix; a matrix just represents a transformation. You can "solve" an equation for the determinant of a matrix through cofactor expansion, which might be what you're talking about. You can't "turn a 5x5 matrix into a 4x4 matrix"; they don't even operate on the same sets.

Here is the method I was given of turning 4x4 to 3x3
 

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Well sam, I see you are talking about partitioning the stiffness matrix when you have a matrix equation relating the vector of forces (loads) to the vector of deflections.

You can do this because you are introducing a compatibility relationship.

Partitioning is not the same as reducing the matrix.

Why did you not post this as an engineering question where it might have been more quickly recognised?

What is the actual problem you are trying to solve? - please name your symbols.

Does this help?

http://algebra.math.ust.hk/matrix_linear_trans/08_partition/lecture.shtml
 
You are able to reduce the size of the matrix because the values of some deflections are known, eg usually zero at supports.

Thus a set of 5 equations can be reduced to four if one deflection is zero.

This is what was meant by insert the zero in your notes.

I cannot say more without more detail.