16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 3.4.1

Linear Transformations

Mathematics — Linear Algebra · matrix-of-transformation-change-of-basis

Problem

Let

T

be the linear operator on

C^2

defined by

T(x_1, x_2) = (x_1, 0)

. Let

\mathfrak{B}

be the standard ordered basis for

C^2

and let

\mathfrak{B}' = \{\alpha_1, \alpha_2\}

be the ordered basis defined by

\alpha_1 = (1, i)

\alpha_2 = (-i, 2)

. (a) What is the matrix of

T

relative to the pair

\mathfrak{B}

\mathfrak{B}'

? (b) What is the matrix of

T

relative to the pair

\mathfrak{B}'

\mathfrak{B}

? (c) What is the matrix of

T

in the ordered basis

\mathfrak{B}'

? (d) What is the matrix of

T

in the ordered basis

\{\alpha_2, \alpha_1\}