Question

I just started and I don't get why they graph the columns x[2 -1], (vertical notation with the [ ]), as if the first number is a x coordinate and the second number is a y coordinate on the graphs Prof. Strang draws. Any help?

Answer 1

In linear algebra, x is often used to denote a matrix, so the x in the equation \[\left[\begin{matrix}2 \\ -1\end{matrix}\right]x = b\] has nothing to do with the x,y coordinates.

The matrix \[\left[\begin{matrix}2 \\ -1\end{matrix}\right]\]is simply a vector in two-dimensional space. Assigning the numbers to the x and y coordinates is somewhat arbitrary, but typically the first number is visually represented as a magnitude on the x coordinate, the second number on the y coordinate . If there was a third number it would be on the z coordinate and so forth.

Again, this is distinct from the variable x which is being multiplied by the matrix \[\left[\begin{matrix}2 \\ -1\end{matrix}\right]\]Please continue watching the videos and doing the exercises and as you become more familiar with matrix multiplication, you will understand what the variable x means.