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

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In summary, you were given a method of transforming a 4x4 matrix to a 3x3 matrix, but you don't understand how to do it. You need to find the determinant of the 5x5 matrix first, and then you can change it into a 4x4 matrix.
  • #1
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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  • #2
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?
 
  • #3
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
 
  • #4
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?
 
  • #5
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.
 
  • #6
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??
 
  • #7
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.
 
  • #8
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.
 
  • #9
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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  • #10
Bumpidy bump
 
  • #11
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
 
  • #12
Studiot said:
Why did you not post this as an engineering question where it might have been more quickly recognised?

He did post it in the engineering forum. But I thought it was a linear algebra problem, so I moved it to the math forums. :redface:
I'll move it back to engineering...
 
  • #13
Oh sorry.

:blushing:
 
  • #14
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.
 

1. What are matrices?

Matrices are mathematical structures consisting of rows and columns of numbers or variables. They are commonly used in linear algebra to represent systems of equations and transformations.

2. How do I perform basic operations on matrices?

To add or subtract matrices, the matrices must have the same dimensions. To multiply matrices, the number of columns in the first matrix must be equal to the number of rows in the second matrix. To find the inverse of a matrix, use Gaussian elimination or row reduction.

3. How are matrices used in real life?

Matrices have many applications in real life, including in computer graphics, economics, physics, and engineering. They are used to model and solve complex systems and to represent data in a structured way.

4. How do I know if two matrices are equal?

Two matrices are equal if they have the same dimensions and all corresponding elements are equal. In other words, if the matrices have the same number of rows and columns and the corresponding elements in each position are equal.

5. Can I perform operations on matrices with different dimensions?

No, basic operations such as addition, subtraction, and multiplication can only be performed on matrices with the same dimensions. However, there are techniques such as padding or truncating matrices that can be used to make them compatible for operations.

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