Suppose T : R³ → R³ has 2-dimensional range and we know T(1,0,0)=(2,1,-1), T(1,1,1)=(0,0,0) Which of the following are a possible standard matrix of T? O 2 10 1 0 2 1 1 1 1 0 0 0 2 1 - 1 -2 0 2 1 BAN 1 1 -3 -2 0
Suppose T : R³ → R³ has 2-dimensional range and we know T(1,0,0)=(2,1,-1), T(1,1,1)=(0,0,0) Which of the following are a possible standard matrix of T? O 2 10 1 0 2 1 1 1 1 0 0 0 2 1 - 1 -2 0 2 1 BAN 1 1 -3 -2 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Suppose \( T : \mathbb{R}^3 \rightarrow \mathbb{R}^3 \) has a 2-dimensional range and we know
\[ T(1,0,0) = (2,1,-1), \quad T(1,1,1) = (0,0,0) \]
Which of the following are a possible standard matrix of \( T \)?
1. \[
\begin{bmatrix}
2 & 1 & 0 \\
1 & 1 & 0 \\
-1 & 1 & 0
\end{bmatrix}
\]
2. \[
\begin{bmatrix}
2 & 1 & -1 \\
1 & 1 & 1 \\
0 & 0 & 0
\end{bmatrix}
\]
3. \[
\begin{bmatrix}
2 & 1 & -3 \\
1 & 1 & -2 \\
-1 & 1 & 0
\end{bmatrix}
\]
4. \[
\begin{bmatrix}
2 & 1 & -1 \\
1 & 1 & 1 \\
-3 & -2 & 0
\end{bmatrix}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd0f3171b-001d-4e71-b013-5e26782f20a2%2Faaa5df28-777e-4d64-b6a4-9fe4602c8c99%2Fmedmres_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose \( T : \mathbb{R}^3 \rightarrow \mathbb{R}^3 \) has a 2-dimensional range and we know
\[ T(1,0,0) = (2,1,-1), \quad T(1,1,1) = (0,0,0) \]
Which of the following are a possible standard matrix of \( T \)?
1. \[
\begin{bmatrix}
2 & 1 & 0 \\
1 & 1 & 0 \\
-1 & 1 & 0
\end{bmatrix}
\]
2. \[
\begin{bmatrix}
2 & 1 & -1 \\
1 & 1 & 1 \\
0 & 0 & 0
\end{bmatrix}
\]
3. \[
\begin{bmatrix}
2 & 1 & -3 \\
1 & 1 & -2 \\
-1 & 1 & 0
\end{bmatrix}
\]
4. \[
\begin{bmatrix}
2 & 1 & -1 \\
1 & 1 & 1 \\
-3 & -2 & 0
\end{bmatrix}
\]
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