- #1

- 753

- 1

$$x_1+x_2+x_3=1$$

and $$x_4+x_5+x_6=1$$

Then they can be put into a matrix representation

\begin{equation*}

\begin{bmatrix}

1 & 1 & 1 & 0 & 0 & 0 \\

0 & 0 & 0 & 1 & 1 & 1\\

\end{bmatrix}

\begin{bmatrix}

x_1 \\

x_2 \\

x_3 \\

x_4 \\

x_5 \\

x_6 \\

\end{bmatrix}

=

\begin{bmatrix}

1 \\

1 \\

\end{bmatrix}

\end{equation*}

So I know that columns in a matrix represent vectors. Is it true that in this matrix we therefore have 6 2D vectors?

Also it looks like there are only 2 vectors, and 3 each of them.

It's just surprising to me that there are 6 variables and only 2D vectors.

If I imagine them to be 2D vectors in x-y plane, then they are also mutually perpendicular. So eventually, the equations I mentioned above, although they look like planes, are they just really the x and y axes?

I guess I'm confused in going from the vector interpretation to the equation interpretation of the matrix.

I would appreciate help in understanding how to interpret the matrix form