A First Course in Linear Algebra · Problem C16

To find a matrix representation, you need to see how the transformation acts on the standard basis vectors of the domain. Apply $T$ to each of $e_1, e_2, e_3$ in $\mathbb{C}^3$—the outputs become the columns of your matrix. This works because any linear transformation is completely determined by where it sends basis vectors, and matrix multiplication distributes that action across coordinates.

To find a matrix representation, you need to see how the transformation acts on the standard basis vectors of the domain. Apply $T$ to each of $e_1, e_2, e_3$ in $\mathbb{C}^3$—the outputs become the columns of your matrix. This works because any linear transformation is completely determined by where it sends basis vectors, and matrix multiplication distributes that action across coordinates.