Hi Duong Cao,
Here's an explanation of this behavior that you're observing:
1] Matrix Division Error:
- When you try 1/[1, 2, 3], MATLAB attempts to perform matrix right division. Here, it interprets the operation as solving the equation x * [1, 2, 3] = 1 for x. This requires the dimensions to be compatible for matrix multiplication, which isn't possible because a scalar (1x1) cannot multiply a row vector (1x3) to produce a scalar (1x1). Hence, you encounter a dimension mismatch error.
2] Pseudo-Inverse Solution:
- When you use 1/[1; 2; 3], MATLAB interprets this as multiplying 1 by the pseudo-inverse of the column vector [1; 2; 3]. This is a valid operation because the pseudo-inverse provides a way to handle non-square matrices, resulting in a least-squares solution. In this case, it returns [0, 0, 0.3333], which satisfies the equation in a least-squares sense.
For more detailed information, you can refer to the MATLAB documentation on matrix right division:
Additionally, you may find this MATLAB Central answer post helpful, as it discusses a similar case:
