Step 1:
Understand that if $\mathbf{x}_1^{\star}$ and $\mathbf{x}_2^{\star}$ are solutions to the linear system $A \mathbf{x} = \mathbf{b}$, then substituting either $\mathbf{x}_1^{\star}$ or $\mathbf{x}_2^{\star}$ into the equation yields $A \mathbf{x}_1^{\star} =
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