Thread: Another matrix as elementary matrices

1. Another matrix as elementary matrices

Hey everyone

I am trying to write this matrix as a product elementary matrices:

$\displaystyle \begin{bmatrix} -3 & 1 \\ 2 & 2 \end{bmatrix}$

I keep on getting this answer:
$\displaystyle \begin{bmatrix} -3 & 0 \\ 0 & 1 \end{bmatrix} \begin{bmatrix} 1 & 0 \\ 2 & 1 \end{bmatrix} \begin{bmatrix} 1 & 0 \\ 0 & \frac4{3} \end{bmatrix} \begin{bmatrix} 1 & -\frac{1}3 \\ 0 & 1 \end{bmatrix}$

I've did it 3 times and keep getting the same answer. Can someone point me to where I am going wrong.

Thanks

2. Can this system be solved?

$\displaystyle \displaystyle \begin{bmatrix} -3 & 0 \\ 0 & 1 \end{bmatrix} \begin{bmatrix} l_{11} & 0 \\ l_{21} & l_{22} \end{bmatrix} \times \begin{bmatrix} u_{11} & u_{12} \\ 0 & u_{22} \end{bmatrix}$

$\displaystyle \displaystyle -3=l_{11}u_{11}$

$\displaystyle \displaystyle 1= l_{11}u_{12}$

$\displaystyle \displaystyle 2=l_{21}u_{11}$

$\displaystyle \displaystyle 2=l_{21}u_{12}+l_{12}u_{22}$

3. Originally Posted by pickslides
Can this system be solved?

$\displaystyle \displaystyle \begin{bmatrix} -3 & 0 \\ 0 & 1 \end{bmatrix} \begin{bmatrix} l_{11} & 0 \\ l_{21} & l_{22} \end{bmatrix} \times \begin{bmatrix} u_{11} & u_{12} \\ 0 & u_{22} \end{bmatrix}$

$\displaystyle \displaystyle -3=l_{11}u_{11}$

$\displaystyle \displaystyle 1= l_{11}u_{12}$

$\displaystyle \displaystyle 2=l_{21}u_{11}$

$\displaystyle \displaystyle 2=l_{21}u_{12}+l_{12}u_{22}$
This the LU Factorization which I informed you of yesterday evant8950.

pickslides, did you mean to write this

$\displaystyle \displaystyle \begin{bmatrix} -3 & 1 \\ 2 & 2 \end{bmatrix}= \begin{bmatrix} l_{11} & 0 \\ l_{21} & l_{22} \end{bmatrix} \times \begin{bmatrix} u_{11} & u_{12} \\ 0 & u_{22} \end{bmatrix}\text{?}$