# Column Vectors:Why?

• December 1st 2007, 10:19 AM
partyshoes
Column Vectors:Why?
3 equations, 3 unknowns x,y,z can be represented by Row Matrix below:

1 2 3
x
10
4 5 6
y
=11
7 8 9
z
12

This can be represented by column vectors:

1
x
4
y
5
etc
7

I am troubled by this idea. The row vectors make sense, but as the columns represent coefficients of the same axis (on 3d coordinate graph) how can these columns be vectors which can themselves be represented on the same style graph. Dr Strang cannot be wrong so there is something I have ommited to understand. Can anyone explain and put me out of my misery?
• December 1st 2007, 11:10 AM
Plato
I truly wish that I could read your question. But as posted, I have no idea about what it could mean. There are three drawbacks to doing mathematics on the web: notation, notation, notation. But happily that is LaTeX for those who are serious. Have you considered learning the basic code?
• December 1st 2007, 01:42 PM
Soroban
Hello, partyshoes!

Are you sure you understand these matrices?

Three equations in three unknowns $(x,y,z)$ can be represented
. . by this Matrix Equation:

. . . . $\begin{pmatrix}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{pmatrix}\,\begin{pmatrix}x \\ y \\ z\end{pmatrix} \;=\;\begin{pmatrix}10 \\11\\12\end{pmatrix}$

This represents three equations:

. . $\begin{pmatrix}1 & 2 & 3\end{pmatrix}\begin{pmatrix}x\\y\\z\end{pmatrix}\ ;=\;10 \quad\Rightarrow\quad x + 2y + 3x \:=\:10$

. . $\begin{pmatrix}4 & 5 & 6\end{pmatrix}\begin{pmatrix}x\\y\\z\end{pmatrix} \:=\:11\quad\Rightarrow\quad 4x + 5y + 6z \:=\:11$

. . $\begin{pmatrix}7 & 8 & 9\end{pmatrix}\begin{pmatrix}x\\y\\z\end{pmatrix} \:=\:12\quad\Rightarrow\quad 7x + 8y + 9z \:=\:12$