How can I find rank of matrix?

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Iva Budan
Iva Budan 2022-6-13
回答： Ayush Singh 2022-6-13
Hi, I don't know how to start solving this task so any answer would be helpful. Thanks
Task
The system of linear algebraic equations is given
7x1+6x2+9x3+2x4=12
7x1+x2+3x3+2x4=0
2x1+x2+5x3+5x4=15
6x1+4x2+2x3+6x4=0
I need to find rank,det,trace,inherent values,eigenvectors of the system coefficient matrix and to solve x1,x2,x3,x4.

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回答（5 个）

Chunru
Chunru 2022-6-13
Ran in:
% Get the coefficient matrix of the system
A = [ 7 6 9 2
7 1 3 2
2 1 5 5
6 4 2 6]
A = 4×4
7 6 9 2 7 1 3 2 2 1 5 5 6 4 2 6
% compute the rank
rank(A)
ans = 4
Bjorn Gustavsson
Bjorn Gustavsson 2022-6-13
First use pen (pencil) and paper to rewrite your equations into a normal matrix-form:
Where M is a 4-by-4 matrix x is an array with your four unknown x1, x2, x3 and x4 and y is your right-hand side.
Once you've done that you should only have to calculate the rank, det, eigenvalues and eigenvectors. That is easily done with the functions: rank, det, trace, and eig. Just look up the help and documentation to each of those functions. (Maybe you're expected to calculate these by hand, if so just use more paper and patience and use matlab for checking your workings-out.)
HTH
Abhishek Chakram
Abhishek Chakram 2022-6-13
Hi Iva,
I understand that you want to find rank, determinant, trace, eigenvalues and eigenvectors of the coefficient matrix.
You can go through these official Mathworks documentations for calculating all the values:
Nitanshu
Nitanshu 2022-6-13
Hi Iva,
You could do this as follows:
First form a matrix of coefficients.
A = [ 7 6 9 2;
7 1 3 2;
2 1 5 5;
6 4 2 6 ]
Then find rank of matrix using this:
rank_A = rank(A)
For the determinant of matrix you can do this:
det_A = det(A)
For the trace of matrix use this:
trace_A = trace(A)
For eigenvalues:
eig_values = eig(A)
Hope it helps !
Ayush Singh
Ayush Singh 2022-6-13
Hi Iva,
From your question I understand you want to find the rank,determinant,trace,inherent values and eigenvectors.
For better understanding of the syntax and the concept I would prefer you to go through the following documentation on
  1. Rank
  2. Determinant
  3. Eigenvectors
  4. Trace
Meanwhile can you please elaborate on what do you mean by "inherent values"?

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