Can both of this vector combine become the following matrix?

1. Feb 21, 2009

RyozKidz

vector A : ai+bj
vector B : ci+dj

can both of this vector combine become the following matrix?

$$\stackrel{a}{c}$$ $$\stackrel{b}{d}$$ or $$\stackrel{a}{b}$$ $$\stackrel{c}{d}$$

2. Feb 21, 2009

John Creighto

Re: matrix

What do you mean by combine?

3. Feb 21, 2009

enricfemi

Re: matrix

do you mean put vectors together in column or in row?

4. Feb 21, 2009

Hootenanny

Staff Emeritus
Re: matrix

You just need to consider the definition of matrix multiplication. You want to find a matrix A such that

$$\left(\begin{array}{c} a\bold{i} + b\bold{j} \\ c\bold{i} + d\bold{j} \end{array}\right) = A \left(\begin{array}{c} \bold{i} \\ \bold{j} \end{array}\right) = \left(\begin{array}{cc} a_{11} & a_{12} \\ a_{21} & a_{22} \end{array}\right) \left(\begin{array}{c} \bold{i} \\ \bold{j} \end{array}\right)$$

From this you should be able to work out the required components.

5. Feb 21, 2009

HallsofIvy

Re: matrix

You can put numbers together any way you please and make a matrix. The question is how do you want that matrix to be related to the original vectors and what do you want to do with it?

6. Feb 23, 2009

RyozKidz

Re: matrix

I think i found the answer by the definition of the mutiplication of matrix...
Thx a lot..~
coz when i read about the article of the transformation matrix i can't get it..hehe thx