Question

Given that the linear map $T: \mathbb{R}^3 \to \mathbb{R}^3$ satisfies $T\begin{pmatrix} -2 \ 1 \ 3 \end{pmatrix} = \begin{pmatrix} 1 \ 0 \ 0 \end{pmatrix}$, $T\begin{pmatrix} -5 \ 2 \ 8 \end{pmatrix} = \begin{pmatrix} 0 \ 1 \ 0 \end{pmatrix}$, and $T\begin{pmatrix} -12 \ 5 \ 20 \end{pmatrix} = \begin{pmatrix} 0 \ 0 \ 1 \end{pmatrix}$, find the value of $T\begin{pmatrix} 39 \ -15 \ -65 \end{pmatrix}$.

          Given that the linear map $T: \mathbb{R}^3 \to \mathbb{R}^3$ satisfies
$T\begin{pmatrix} -2 \ 1 \ 3 \end{pmatrix} = \begin{pmatrix} 1 \ 0 \ 0 \end{pmatrix}$, $T\begin{pmatrix} -5 \ 2 \ 8 \end{pmatrix} = \begin{pmatrix} 0 \ 1 \ 0 \end{pmatrix}$, and $T\begin{pmatrix} -12 \ 5 \ 20 \end{pmatrix} = \begin{pmatrix} 0 \ 0 \ 1 \end{pmatrix}$,
find the value of $T\begin{pmatrix} 39 \ -15 \ -65 \end{pmatrix}$.

Given that the linear map T: ℝ^3 →ℝ^3 satisfies
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 >, and T
< p m a t r i x >
=
< p m a t r i x >,
find the value of T
< p m a t r i x >.

Added by Katherine G.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Danielle Fairburn

06/05/2024

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Given that the linear map $T: \mathbb{R}^3 \rightarrow \mathbb{R}^3$ satisfies $$T \left( \begin{pmatrix} -2 \\ 1 \\ 3 \end{pmatrix} \right) = \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix}, T \left( \begin{pmatrix} -5 \\ 2 \\ 8 \end{pmatrix} \right) = \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix}, \text{and} T \left( \begin{pmatrix} -12 \\ 5 \\ 20 \end{pmatrix} \right) = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix},$$ find the value of $T \left( \begin{pmatrix} 39 \\ -15 \\ -65 \end{pmatrix} \right)$.