A certain linear circuit has four input voltages and one output voltage \(v_{\mathrm{O}}\). The following table lists the output for different values of the four inputs. Find the input-output relationship for the circuit. Specifically, find an expression for \(v\) o in terms of the four input voltages. Then draw a block diagram of the circuit.

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US1 (V) VS2 (V) VS3 () VS4 V vo (V) 2 -4 1 20 1 2 2 3 1 0 4 2 4 5 1.5 2 -1 -4 -1 3