{e₁,e2, e3} be the standard basis of R³ and let f,g : R³ → R³ be the linear map 1. Let E = satisfying¹ We define f(e₁) = cos() e₁ + sin (7) €₂ ƒ(e₂) = = sin() e₁ + cos f(3) = e₂ = -e3 *-{0-0-0} B = g(e₁) =e₁ g(e₂) = ₁ + g(e3) = ₁ + which is a basis of R³. (a) Explain why f and g are well-defined. ₂ ₂ + €3

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