Hello! In lecture 1, on the column picture , professor visualizes a vector using corersponding 'x' and 'y' co-efficients of two equations.
2x-y=0
-x+2y=3
While i get the row picture (as points on a xy plane), how can x (or y )co-efficients alone of the eqn be graphed on 2 separate dimensions? what am i missing ?
Also why is the column of unknowns col matrix [x y] called a vector?

Question

Hello! In lecture 1, on the column picture , professor visualizes a vector using corersponding 'x' and 'y' co-efficients of two equations.  
2x-y=0
-x+2y=3
While i get the row picture (as points on a xy plane), how can x (or y )co-efficients  alone of the eqn be graphed on 2 separate dimensions? what am i missing ?
Also why is the column of unknowns col matrix [x y] called a vector?

anonymous · Answer

Since vector is just an array of numbers the columns can be seen as vectors. But these vectors are not in the same dimension/plane as the unknowns are. Let's call them $$\left[\begin{matrix}\dim1 \ \dim2\end{matrix}\right]$$

anonymous · Answer

Please correct me if am wrong. All the co-efficients of a single equation can be said to belong to a single dimension according to the column picture. And the dimension of one equation's coefficients is always different from the other. Is there any intuitive way of understanding it?

anonymous · Answer

Yes you have said it correct. Instead of unknowns being the dimensions, in column picture,  equations are the dimensions.

anonymous · Answer

Do you know how to solve the problem or find unknowns by column picture? Do we have to search the whole n-dimensional space?

anonymous · Answer

Am afraid so. I dont see the column picture to be helpful in solving unknowns(Cos even the Professor takes the right values of unknowns directly for explanation). But i may be wrong. Let's see as the course progresses.