Why does this error happen? [Warning: Rank deficient, rank = 2, tol = 1.850312e-14.]

Why does this error happen?

A = [1 2 3; 4 5 6; 7 8 9; 10 11 12]

A =

1 2 3

4 5 6

7 8 9

10 11 12

A/A

[Warning: Rank deficient, rank = 2, tol = 1.696862e-14.]

ans =

1.0000 0 0 0

0.6667 0 0 0.3333

0.3333 0 0 0.6667

0.0000 0 0 1.0000

Answer 1

[Ameer Hamza]

The matrix A is not invertible. If you calculate the reduced row echelon of this matrix, you will see that it only have two linearly independent rows

>> A = [1 2 3; 4 5 6; 7 8 9; 10 11 12];
>> rref(A)
ans =
     1     0    -1
     0     1     2
     0     0     0
     0     0     0

MATLAB error indicates that because of this issue, the result of inversion will be incorrect.

[Isabel Muñiz]

Thank you very much!

[Ameer Hamza]

I am glad to be of help!!!