# How can I find rank of matrix?

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Iva Budan on 13 Jun 2022
Answered: Ayush Singh on 13 Jun 2022
Hi, I don't know how to start solving this task so any answer would be helpful. Thanks
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. Chunru on 13 Jun 2022
% 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 on 13 Jun 2022
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 on 13 Jun 2022
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 on 13 Jun 2022
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 on 13 Jun 2022
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
Meanwhile can you please elaborate on what do you mean by "inherent values"?