Yes.
Proof: Consider x, y in R^m. Then since T is linear, we have:
T(a x + b y) = a T(x) + b T(y)
But since L is linear, we have:
L(a T(x) + b T(y)) = a L(T(x)) + b L(T(y))
So:
L(T(a x + b y)) = a L(T(x)) + b L(T(y))
and the composition is linear.
The transformation z = L ( T ( x )) is linear because it satisfies both additivity and homogeneity properties that define linear transformations. Since both T and L are linear, their composition is also linear. Thus, we confirm z = L ( T ( x )) is a linear transformation.
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Jawab:Penjelasan dengan langkah-langkah:Rata-rata dari x dan y adalah -10.Penjelasan: Rata-rata dari x, y, dan 30 adalah 10: Ini berarti (x + y + 30) / 3 = 10.Kalikan kedua sisi dengan 3: x + y + 30 = 30.Kurangkan 30 dari kedua sisi: x + y = 0.Rata-rata x dan y: (x + y) / 2 = 0 / 2 = 0.