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$$\begin{bmatrix}-1 & 2 & -5\\2 & -1 & 6\\ 2 & -2 & 7\end{bmatrix}$$

What i did was multiply the first line by 2 =
$$\begin{bmatrix}-1 & -2 & -5\end{bmatrix} * 2 = \begin{bmatrix}-2 & 4 & -10\end{bmatrix}$$
So here i added the first line multiplied by 2 to the second and third ones to create zeroes 
$$\begin{bmatrix}-1 & -2 & -5\end{bmatrix}$$
$$\begin{bmatrix}2 & -1 & 6\end{bmatrix} + \begin{bmatrix}-2 & 4 & -10\end{bmatrix}$$ 
$$\begin{bmatrix}2 & -2 & 7\end{bmatrix}+ \begin{bmatrix}-2 & 4 & -10\end{bmatrix}$$

Resulting in
$$\begin{bmatrix}-1 & 2 & -5\\0 & 3 & 4\\ 0 & 2 & 3\end{bmatrix}$$

Finally i changed this second line so i could eliminate the third line's y variable:

$$\begin{bmatrix}0 & 3 & 4\end{bmatrix} * 2/3 = \begin{bmatrix}0 & 6/3 & 8/3\end{bmatrix}$$

As 6/3 equals 2

$$\begin{bmatrix}0 & 3 & 4\end{bmatrix} * 2/3 = \begin{bmatrix}0 & 2 & 8/3\end{bmatrix}$$

and with this line i could finish it:

$$\begin{bmatrix}0 & 2 & 9/3\end{bmatrix} - \begin{bmatrix}0 & 2 & 8/3\end{bmatrix} = \begin{bmatrix}0 & 0 & 1/3\end{bmatrix} $$

So i'll end up with

$$\begin{bmatrix}-1 & 2 & -5\\0 & 3 & 4\\ 0 & 0 & 1/3\end{bmatrix}$$

Mon, 25 Nov 2013 18:39 GMT