I am reading a book on Linear Algebra
On page 47, the author introduces the concept of matrix times a vector as follows:
At this point, the author hasn't introduced the concept of matrix multiplication.
Can someone explain what's going on in the highlighted part? Particularly, I have trouble understanding -> (2 2) (x y) part. As I said, the author hasn't introduced matrix multiplication at this point. Is he going to solve this using dot product?
Best Answer
They are multiplying first with first, second with second etc. and then adding them together, like in the dot product. In general, $$\begin{pmatrix}x_1&x_2&\cdots&x_n\end{pmatrix}\begin{pmatrix}y_1\\y_2\\ \vdots\\y_n\end{pmatrix}=x_1y_1+x_2y_2+\ldots+x_ny_n$$