Question

Let T be the linear operator on c2 defined by

T(Q1, 22) = (2iai + 3a,, aj az) If B is the standard ordered
basis for ca the Tlg is​

Answer 1

The matrix representation of the linear operator T with respect to the standard ordered basis B for C2 is [[2i, 3], [0, 0]].

Step-by-step explanation:

The student's question relates to a linear algebra problem involving a linear operator T on C2. The question asks to determine the matrix representation of T with respect to the standard ordered basis for C2, denoted B. To find this matrix representation, one must apply T to each vector in the standard basis and then write the output as a column in the matrix [T]B.

First, apply T to the first standard basis vector, (1, 0), which gives T(1, 0) = (2i*1 + 3*0, 1*0 + 0*0) = (2i, 0). Next, apply T to the second standard basis vector, (0, 1), yielding T(0, 1) = (2i*0 + 3*1, 0*1 + 1*0) = (3, 0).

Thus, the matrix representation of T with respect to the standard ordered basis B is:

[T]B =
[[2i, 3],
[0, 0]]