How can I solve 16x16 matrix? It is specifically required to solve Ax=b matrix.

Here I am giving my code

A = [1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0
     1     1     1     1     1     1     1     1     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     0     0     1     1     1     1     1     1     1     1
     0     0     0     0     0     0     0     0     1     1     1     1     1     1     1     1
     0     1     2     3     4     5     6     7     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     0     0     0     1     2     3     4     5     6     7
     0     0     2     6    12    20    30    42     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     0     0     0     0     2     6    12    20    30    42
     0     0     0     6    24    60   120   210     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     0     0     0     0     0     6    24    60   120   210
     0     0     0     0    24   120   360   840     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     0     0     0     0     0     0    24   120   360   840
     0     1     2     3     4     5     6     7     0    -1    -2    -3    -4    -5    -6    -7
     0     0     2     6    12    20    30    42     0     0    -2    -6   -12   -20   -30   -42
     0     0     0     6    24    60   120   210     0     0     0    -6   -24   -60  -120  -210
     0     0     0     0    24   120   360   840     0     0     0     0   -24  -120  -360  -840]
 b= [0
     1
     1
     2
     0
     0
     0
     0
     0
     0
     0
     0
     0
     0
     0
     0]
x = [
 a10
 a11
 a12
 a13
 a14
 a15
 a16
 a17
 a20
 a21
 a22
 a23
 a24
 a25
 a26
 a27]

So, how can I solve it?

Answer 1

[Walter Roberson]

Your fourth row is the same as the third. The third row is 1 minus the second.

rank(A) is only 11 (out of possible 16). You cannot use the normal technique which would be

x = A\b;

There is no unique solution.

One of the non-unique solutions is

x = pinv(A) * b;

[Maidul Islam]

Thanks a lot Walter Roberson!!! I'm grateful to you.