Where do the coefficients in this vector equation come from?

[mathsdespair]

x1 1 1 0 0
x2 0 0 1 1
x3 = 1 + -1 + 0 + 0 Each of these numbers in vertical form are meant to be
x4 0 0 1 -1 vectors

Where do these coefficients come from 0.5(x1+x3) 0.5(x1-x3) 0.5(x2+x4) 0.5(x2=x4)
The first coefficient goes in front of vector one and so on..

Thanks

 

[mathman]

I think you should start from the beginning. Also fix typos.

 

[HallsofIvy]

It's impossible to tell what you mean. I presume that you intended to say
$$\begin{bmatrix}x_1 & x_2 & x_3 & x_4\end{bmatrix}= \begin{bmatrix}1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1 \\ 1 & -1 & 0 & 0 \\ 0 & 0 & 1 & -1\end{bmatrix}$$
or
$$\begin{bmatrix}x_1 \\ x_2 \\ x_3 \\ x_4\end{bmatrix}= \begin{bmatrix}1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1 \\ 1 & -1 & 0 & 0 \\ 0 & 0 & 1 & -1\end{bmatrix}$$ But I don't know what "0.5(x1+x3) 0.5(x1-x3) 0.5(x2+x4) 0.5(x2=x4)" is supposed to mean. I presume that last is supposed to be "x2- x4". What were those terms supposed to equal?