tweak
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"\n",
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"Now, $A$ is $m \\times 2$, and full column rank (assuming distinct voltages $|d_k|$), but of course it is not invertible for $m > 2$.\n",
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"\n",
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"It will still have a solution (a unique solution!) if all of the $R_k$ measurements fall *exactly* on a quadratic curve $x_1 + x_2 d^2$, but in a real experiment there would be some *measurement noise* that would spoil this.\n",
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"It will still have a solution (a unique solution!) if all of the $R_k$ measurements fall *exactly* on a quadratic curve $x_1 + x_2 d^2$, but in a real experiment there would be some *measurement noise* that would spoil this. (There will also be *systematic errors* because real resistors are not exactly quadratic, but let's ignore that here.)\n",
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"\n",
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"For example, let's suppose $x = (1,2)$ and we do $m=200$ measurements for $d \\in [0,2]$, but that each measurement has a random uncertainty $\\approx R \\pm 0.1$."
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