Homework Help: A question on vector placing

1. Feb 29, 2008

transgalactic

in previous question
i was tald that in the proccess of building the transformation matrix

i should have put the vectors of the new base as columns and not as rows

in what cases and in what formes i put them as rows??
in what cases and in what formes i put them as columns??

2. Mar 1, 2008

regards

marco

3. Mar 1, 2008

CompuChip

Also, you can always check by applying the transformation matrix to one of your basis elements. If you want A to transform the vector v into the vector w, you can check that indeed
Av = w
and/or
A-1 w = v.

For example, if you write down a general matrix
$$A = \begin{pmatrix} a_{11} & a_{12} & \cdots \\ a_{21} & a_{22} & \cdots \\ \vdots & \ddots & \cdots \end{pmatrix}$$
you can apply it to the (old) basis vector
$$e_1 = \begin{pmatrix} 1 \\ 0 \\ 0 \\ \vdots \end{pmatrix}$$
and just do the multiplication explicitly. You will get a result expressed in the $a_{ij}$ which will in fact be just a complete row or column from A. On the other hand, it should also be the new basis vector. So you can read off whether you need to put it in a column, or in a row.

4. Mar 1, 2008

transgalactic

can you give an actual example to this
and in simpler words

because i cant understand how this multiplication effects the desition to put the vectors by rows or by columns

using your multiplication i would get the first row of this matrix
now what??

5. Mar 1, 2008

HallsofIvy

He said: "Try both and see which gives what you want!"