# Thread: another matrix problem :( sorry

1. ## another matrix problem :( sorry

hey guys- these type of questions I dont even know where to begin..

Suppose a 3 x 3 matrix A can be transofrmed into a 3 x 3 matrix B by the following row operations;

R2 = R2 - 2R1 , R2 <--> (interchange) R3 and R3 = 1/3 R3

and that E F and G are the corresponding elementary matrices

a) write down the matrices E F G and express B in terms of A E F G ??
B) if det(a) =/= 0 then find det(b)/det(a)

What does all that mean- I didn't understand a single word what that question or even the information was telling me....

can some one explain it to me and also do the working out thanks

I dont understand the question nor the information....

First I started off like this

A = ( a b c )
( d e f )
( g h i )

I applied all those row operations and then i completly lost it

Can someone explain to what is elementry matrix ? I tried wikipedia but still coudn't understand it and also what exactly does the question even mean....

2. Originally Posted by Khonics89
hey guys- these type of questions I dont even know where to begin..

Suppose a 3 x 3 matrix A can be transofrmed into a 3 x 3 matrix B by the following row operations;

R2 = R2 - 2R1 , R2 <--> (interchange) R3 and R3 = 1/3 R3

and that E F and G are the corresponding elementary matrices

a) write down the matrices E F G and express B in terms of A E F G ??
B) if det(a) =/= 0 then find det(b)/det(a)

What does all that mean- I didn't understand a single word what that question or even the information was telling me....

can some one explain it to me and also do the working out thanks

I dont understand the question nor the information....

First I started off like this

A = ( a b c )
( d e f )
( g h i )

I applied all those row operations and then i completly lost it

Can someone explain to what is elementry matrix ? I tried wikipedia but still coudn't understand it and also what exactly does the question even mean....
In a nut shell what they are trying to show is that elementry row operations can be represented as matrix multiplication.

Example take the identity matrix

$\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$

If we multiply row 1 by -2 and add it to row 2 we get

$E_1=\begin{bmatrix} 1 & 0 & 0 \\ -2 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$

$E_2=\begin{bmatrix} 1 & 0 & 0 \\ 0 & 0& 1 \\ 0 & 1 & 0\end{bmatrix}$

$E_3=\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & \frac{1}{3}\end{bmatrix}$

Now for example consider the generic matrix

$\begin{bmatrix} a & b & c \\ d & e & f \\ h& i & j\end{bmatrix}$

If I multiply row 1 by -2 and add it to row 2 I get

$A=\begin{bmatrix} a & b & c \\ d-2a & e-2b & f-2c \\ h& i & j\end{bmatrix}$

Now try it by matrix multiplication(have fun)

$B=\begin{bmatrix} 1 & 0 & 0 \\ -2 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix} \begin{bmatrix} a & b & c \\ d & e & f \\ h& i & j\end{bmatrix}$

If you do this you will get the same thing.... so in matrix format

$B=E_1A$

I hope this helps get you started