In the Deep Learning Book, I encountered this:
To analyze how many solutions the equation has, we can think of the columns of $A$ as specifying different directions we can travel from the origin (the point specified by the vector of all zeros), and determine how many ways there are of reaching $b$. In this view, each element of x specifies how far we should travel in each of these directions.
1) shouldn't it be rows of $A$ instead of columns of $A$? Wouldn't the columns of $A$ be just numbers from different equations realted to one Dimension like $X$, $Y$,...
2) with above definition,is this formula correct?:
Ax = $\sum_{i} x_iA_{:,i}$
how is the sum becomes a vector?
Thank you