Final answer:
In linear algebra, the matrix representation of a linear operator can be found by choosing a basis for both the domain and the codomain and computing the linear combination of basis vectors resulting from applying the linear operator to each basis vector.
Step-by-step explanation:
In linear algebra, a linear operator is a mapping between vector spaces that preserves linear structures.
To find the matrix representation of a linear operator, you need to choose a basis for both the domain and the codomain. Then, the entries of the matrix correspond to the coefficients of the linear combination of basis vectors that result from applying the linear operator to each basis vector.
For example, if we have a linear operator T that maps a 2-dimensional space to another 2-dimensional space, and the standard basis vectors are chosen as the basis, the matrix representation of T can be found by computing T(e1), T(e2), where e1 and e2 are the standard basis vectors of the domain, and expressing them as linear combinations of the basis vectors of the codomain. The resulting coefficients form the matrix representation of T.