Let f and g be two-variable real-valued functions and T; : R R, i = 1,2....

 

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Let f and g be two-variable real-valued functions and T; : R² R, i = 1,2. Suppose that T : R² → R² by T(a₁, a2) = (f(a₁, a2), g(a₁, a2)). Is it true that T is linear iff both T₁(a₁, a2) = f(a₁, a2) and T2(a1, a2) = g(a1, a2) are linear? Let f and g be two-variable real-valued functions and T; : R² R, i = 1,2. Suppose that T : R² → R² by T(a₁, a2) = (f(a₁, a2), g(a₁, a2)). Is it true that T is linear iff both T₁(a₁, a2) = f(a₁, a2) and T2(a1, a2) = g(a1, a2) are linear?

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