(Solved): Cross product is a linear transformation from \( \mathbb{R}^{3} \rightarrow \ ...

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Cross product is a linear transformation from \( \mathbb{R}^{3} \rightarrow \mathbb{R}^{3} \) Define the linear transformation \( T \) as \[ T(\vec{x})=\vec{x} \times\left[\begin{array}{l} 1 \\ 2 \\ 3 \end{array}\right] \] a. Compute \( T\left(\overrightarrow{e_{1}}\right), T\left(\overrightarrow{e_{2}}\right), T\left(\overrightarrow{e_{3}}\right) \) b. Use your answer from a. to write the standard matrix of the linear transformation \( T \) c. Use your answer from b. to compute \( T\left(\left[\begin{array}{c}4 \\ -1 \\ 3\end{array}\right]\right) \)