ok quick question.... why in system of equation is it the x y z are written in such a way across

but in others the it is in written x

y

z

vertically?

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- Oct 13th 2009, 04:45 PM #1

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- Oct 14th 2009, 05:25 AM #2

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Its pretty much convention but sometimes we want to distinguish between "row vectors" and "column vectors" because we want to treat them as matrices. We can multiply $\displaystyle \begin{pmatrix}a & b & c\end{pmatrix}\begin{pmatrix}d \\ e\\ f\end{pmatrix}$ or $\displaystyle \begin{pmatrix}a \\ b \\ c\end{pmatrix}\begin{pmatrix}d & e & f\end{pmatrix}$ but we cannot multiply $\displaystyle \begin{pmatrix}a \\ b \\ c\end{pmatrix}\begin{pmatrix}d \\ e\\ f\end{pmatrix}$ or $\displaystyle \begin{pmatrix}a & b & c\end{pmatrix}\begin{pmatrix}d & e & f\end{pmatrix}$.

To multiply matrices the number of columns of the first must equal the number of rows of the second. In the first example above those are both 3 and in the second example they are both 1. In the the third example, the number of columns in the first matrix is 1 and the number of rows in the second is 3. In the fourth example, the number of columens in the first matrix is 1 and the number of rows in the second is 1.