(b) (5%) Let \( L(\vec{x}) = (2\vec{x}1 - \vec{x}2 - \vec{x}3, \vec{x}1 + 2\vec{x}2 - \vec{x}3)^{\mathrm{T}} \) be the transformation from \( R^3 \) to \( R^2 \). Determine the standard matrix representation \( A \) of the above transformation and find \( L(\vec{x}) \) for \( \vec{x} = (1, 2, 3)^{\mathrm{T}} \).

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