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for it to be linear, T[kx(t)] = kT[x(t)] so i have

T[kx(t)] = kx(t) + [tex]\int[/tex] (t - [tex]\tau[/tex])x([tex]\tau[/tex])d[tex]\tau[/tex]

and

kT[x(t)] = k[x(t) + [tex]\int[/tex] (t - [tex]\tau[/tex])x([tex]\tau[/tex])d[tex]\tau[/tex]] = kx(t) + k[tex]\int[/tex] (t - [tex]\tau[/tex])x([tex]\tau[/tex])d[tex]\tau[/tex]

so they aren't equal and aren't linear. however, i'm not sure about this answer because for the first part, T[kx(t)], i'm not sure if x([tex]\tau[/tex]) should also be multiplied by k, making it a linear system

any help would be appreciated. thx.