$7.$ Op$-$amp summing amplifier

a$)$ Ideally, what should the output voltage of an op$-$amp do if the non$-$inverting voltage is greater $($more positive$)$ than the inverting voltage?

b$)$ Design an op$-$amp circuit that performs the operation Vo$=-$VR $[$B$1\mathrm{.}2-1+$B$2.2-2+$B$3\mathrm{.}2-3+$B$4.2-4].$

c$)$ The op$-$amp circuit output is Vo$=-4$Va$-$Vb$-5$Vc$.$ Given Va$=2$v$,$ Vc$=-1$v$,$ and using $12$v power supplies and an ideal op$-$amp. Determine the value of Vb that allows the op$-$amp to operate in the linear region.