Question

x is arbitrary vector in R^n, y is fixed vector. Prove that T(x)=x.y is a linear tranformation (x.y is dot product)

Answer 1

for all x and x' in R^n and all scalars k,T(x+x')=(x+x')y=xy+x'y=T(x)+T(x') and T(kx)=kxy=kT(x) therefore T is a linear transformation

Answer 2

Thank you. This works for dot product as well as regular multiplication? Why does this proof stuff confuse me?