"Linear Algebra and its Applications"-matrix equation

Matrix equation:

We have previously introduced the linear combination of vectors, the form of X1a1+x2a2+xnan, that we can use to express them with [] formulas. (This expression is sought for convenience and unity of computation), and we give the following definition to give another form of the linear combination of vectors.

It can be seen that the right side of the equation, the form of a vector combination, we use the algebraic nature of the vector to sum it, we will eventually get a vector B, that the equation can be written in the form of ax=b, and easy to see, a written in [A1,a2,... an] form, AI is also a vector, That is, A is a matrix of M x N (m represents the component number of a vector, that is, the r^m vector) and B is one of the vector r^m, which is called the matrix equation. It can be seen that this process is completely self-consistent with the product operation of the matrix that will be introduced later.

For the solution of matrix equation, we can easily convert it into vector equation and linear equations, so we get the following theorem.

"Linear Algebra and its Applications"-matrix equation