Another way to think the matrix mulitply
Usually, we think the matrxi multiply as follows:
Also, we can get the result by :
This kind of operation is just like the linear combination. So when consider the solutions of such $Ax = b$, it is equivalent to find whether we can find any linear combination to construct the $b$.
Take an example:
The equation has a solution if and only if $b$ lies on the plane where $A{:,1} and A{:,2}$linear combination
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