finding space basis in matlab

hello!i am new to matlab and i really would appreciate your help. I need to make a funtion into which i can put an mxn table. This function will find the basis of the space R(A) and the basis of space R(A').

[madhan ravi]

what's R? what's A? what's your desire output ? Give an example ?

[ne ne]

A is an mxn table. I have to make this function in order for it to be used in any table given.

R is a space that contains all of the vectors of A.

for example I have to put the table A=[3 -1 7 3 9; -2 2 -2 7 5; -5 9 3 3 4; -2 6 6 3 7 ]

Answer 1

[John D'Errico]

A=[3 -1 7 3 9; -2 2 -2 7 5; -5 9 3 3 4; -2 6 6 3 7 ]

A is a matrix, not a table. This is a table:

T = table(A)
T =
  4×1 table
                A             
    __________________________
     3    -1     7     3     9
    -2     2    -2     7     5
    -5     9     3     3     4
    -2     6     6     3     7

If you have actually stored A as a table, then you can extract the data from it using table2array. Regardless, if all you want to do is form the row and column basis representations for a matrix A, this is easy enough. Just use orth, twice.

Note that A was 4x5, but with a rank of 3, as we learn here:

rank(A)
ans =
     3

So each basis system will have three basis vectors. The row space of A is spanned by three row vectors:

orth(A.').'
ans =
      0.16491     -0.45832     -0.42192      -0.3853     -0.66051
      0.55328     -0.63554      0.38877    -0.062596       0.3673
    0.0042955     -0.31674     -0.62059      0.68313      0.21877

And the column space of A is spanned by three column vectors.

orth(A)
ans =
     -0.48382      0.79099    0.0005431
     -0.34036     -0.17083      0.92116
     -0.53232     -0.58716     -0.25742
     -0.60556    -0.019817      -0.2919

[John D'Errico]

@SAJJA BALA KARTHIKEYA asked a question (which I have moved into this comment):

"how to find row space of a matrix?"

First, this is not an answer to the question. It is just another question, saying that you did not understand my answer.

But then I would be forced to ask what did I mean when I explicitly stated the solution in my answer:

The row space of A is spanned by the row vectors:

orth(A.').'

As such, your question (asked as an answer) already had an answer.