Question

If $T: \mathbb{R}^3 \rightarrow \mathbb{R}^3$ is a linear transformation such that $T\begin{pmatrix} 1 \ 0 \ 0 \end{pmatrix} = \begin{pmatrix} -2 \ 1 \ 2 \end{pmatrix}$, $T\begin{pmatrix} 0 \ 1 \ 0 \end{pmatrix} = \begin{pmatrix} -4 \ 4 \ 1 \end{pmatrix}$, $T\begin{pmatrix} 0 \ 0 \ 1 \end{pmatrix} = \begin{pmatrix} -1 \ 3 \ -2 \end{pmatrix}$, then $T\begin{pmatrix} 0 \ 1 \ 3 \end{pmatrix} = \begin{pmatrix} -7 \ 13 \ -5 \end{pmatrix}$

          If $T: \mathbb{R}^3 \rightarrow \mathbb{R}^3$ is a linear transformation such that
$T\begin{pmatrix} 1 \ 0 \ 0 \end{pmatrix} = \begin{pmatrix} -2 \ 1 \ 2 \end{pmatrix}$, $T\begin{pmatrix} 0 \ 1 \ 0 \end{pmatrix} = \begin{pmatrix} -4 \ 4 \ 1 \end{pmatrix}$, $T\begin{pmatrix} 0 \ 0 \ 1 \end{pmatrix} = \begin{pmatrix} -1 \ 3 \ -2 \end{pmatrix}$,
then $T\begin{pmatrix} 0 \ 1 \ 3 \end{pmatrix} = \begin{pmatrix} -7 \ 13 \ -5 \end{pmatrix}$

If T: ℝ^3 →ℝ^3 is a linear transformation such that
T
< p m a t r i x >
=
< p m a t r i x >, T
< p m a t r i x >
=
< p m a t r i x >, T
< p m a t r i x >
=
< p m a t r i x >,
then T
< p m a t r i x >
=
< p m a t r i x >

Added by Michael S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Vishal Parmar

04/04/2022

Step 1

We are told that T is a linear transformation from IR3 (the set of all 3-dimensional vectors with real number entries) to R3 (the set of all 3-dimensional vectors with real number entries). We are also given that T(r) = r for all vectors r in IR3. Show more…

Show all steps