Question

In the first lecture on the "column method" why is the x coefficent vector, V1, plotted on the XY plane? V1 should have nothing to do with Y.

Answer 1

I watched that video ages ago, so I can't remember, but my best guess is it is one of those cases where he is reusing the variable name x. The x for the cofficient vector must not be the same x on the xy plane.

For an example suppose I was multiplying the two matrices below
\[\begin{bmatrix}
1& 2\\
3 &4
\end{bmatrix}\begin{bmatrix}x
\\ y

\end{bmatrix}\] The first column in the first matrix is multiplying x, but if I wanted to show it's vector representation on a coordinate plane it would look like the picture below. Maybe it would be clearer to use separate variable names.