# 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

Staff Emeritus
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