Solution pauli matrices can be written as
σx=(0110)\sigma_x=\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}σx=(0110)
σy=(0−ii0)\sigma_y=\begin{pmatrix} 0 & -i\\ i & 0 \end{pmatrix}σy=(0i−i0)
i is iota.
And
σz=(100−1)\sigma_z=\begin{pmatrix} 1 & 0\\ 0 & -1 \end{pmatrix}σz=(100−1)
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