Review Note

\(Ax = \)\(\begin{bmatrix} 1 & 0 & 0\\ -1 & 1 & 0\\ 0 &-1 &1\end{bmatrix}\)\(\begin{bmatrix} x_1\\ x_2\\ x_3\end{bmatrix}\)= \(\begin{bmatrix} x_1\\ x_2 - x_1\\x_3-x_2 \end{bmatrix}\)= \(\begin{bmatrix} b_1\\ b_2\\ b_3\end{bmatrix}\)= \(b\)

The input is \(x\) and the output is \(b = Ax\). This \(A\) is a "difference matrix" because \(b\)
contains differences of the input vector \(x\).