題組內容

5. Define a mapping from $\mathbf{R}^3$ to $\mathbf{R}^2$: $L(\mathbf{x}) = (2x_2 + 5x_3, 3x_1 + x_2)^7$.

(b)(5%) Find a matrix \( \mathbf{A} \) such that \( L(\mathbf{x}) = \mathbf{A}\mathbf{x} \) for each \( \mathbf{x} \in \mathbb{R}^3 \).