題組內容
5. (15%) Let the mapping \( L: \mathbb{R}^3 \to \mathbb{R}^2 \) be defined by: \( L(\mathbf{x}) = (x_1 + 2x_2, \ 3x_2 + x_3 )^{\text{T}} \).
(a) Show that the mapping \( L \) is a linear transformation.
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5. (15%) Let the mapping \( L: \mathbb{R}^3 \to \mathbb{R}^2 \) be defined by: \( L(\mathbf{x}) = (x_1 + 2x_2, \ 3x_2 + x_3 )^{\text{T}} \).
(a) Show that the mapping \( L \) is a linear transformation.