Can both of this vector combine become the following matrix?

[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}


hope anyone can tell me more about this..coz i search a lot a wiki there..~~

 

[John Creighto]

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}


hope anyone can tell me more about this..coz i search a lot a wiki there..~~

What do you mean by combine?

 

[enricfemi]

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

 

[Hootenanny]

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}


hope anyone can tell me more about this..coz i search a lot a wiki there..~~

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

\left(\begin{array}{c}<br /> a\bold{i} + b\bold{j} \\<br /> c\bold{i} + d\bold{j}<br /> \end{array}\right) = A \left(\begin{array}{c}<br /> \bold{i} \\<br /> \bold{j}<br /> \end{array}\right) = <br /> \left(\begin{array}{cc}<br /> a_{11} &amp; a_{12} \\<br /> a_{21} &amp; a_{22}<br /> \end{array}\right)<br /> \left(\begin{array}{c}<br /> \bold{i} \\<br /> \bold{j}<br /> \end{array}\right)

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

 

[HallsofIvy]

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?

 

[RyozKidz]

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