Find all x in R4 that are mapped into the zero vector by the transformation X-Ax for the given matrix A. 128 -1 102-5 A = Select the correct choice below and fill in the answer box within your choice. A. O 013 4 -248 14 B. There is only one vector, which is x = X3 C. X₁ OD. X₁ +X3 +x₂ + X4 - 3 O
Find all x in R4 that are mapped into the zero vector by the transformation X-Ax for the given matrix A. 128 -1 102-5 A = Select the correct choice below and fill in the answer box within your choice. A. O 013 4 -248 14 B. There is only one vector, which is x = X3 C. X₁ OD. X₁ +X3 +x₂ + X4 - 3 O
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.5: Basis And Dimension
Problem 66E
Related questions
Question
is this correct?
![---
### Finding Vectors in \(\mathbb{R}^4\) for the Transformation \(\mathbf{x} \rightarrow A\mathbf{x} \)
Given matrix \(A\):
\[
A = \begin{pmatrix}
1 & 2 & 8 & -1 \\
1 & 0 & 2 & -5 \\
0 & 1 & 3 & 4 \\
-2 & 4 & 8 & 14
\end{pmatrix}
\]
The task is to find all vectors \(\mathbf{x} \in \mathbb{R}^4\) that are mapped into the zero vector by the transformation \(\mathbf{x} \rightarrow A\mathbf{x} \).
---
#### Question
Select the correct choice below and fill in the answer box within your choice.
A.
There is only one vector, which is \(\mathbf{x}\) =
\[
\begin{pmatrix}
-2 \\
-3 \\
1 \\
0 \\
\end{pmatrix}
\]
---
B. (empty box for selection)
---
C. (empty boxes for selection and entry)
\[
\begin{pmatrix}
x_1 \, (empty box) \, + \, x_3 \\
\, (empty box) + \, x_4 \, (empty box)
\end{pmatrix}
\]
---
D. (empty boxes for selection and entry)
\[
\begin{pmatrix}
x_1 \, (empty box) + \\
x_2 \, (empty box)
\end{pmatrix}
\]
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b6c3689-2b60-4c25-801e-fccc9acdd031%2F7ddc4430-792d-458d-b815-39e606d83060%2Fgxrhqsg_processed.png&w=3840&q=75)
Transcribed Image Text:---
### Finding Vectors in \(\mathbb{R}^4\) for the Transformation \(\mathbf{x} \rightarrow A\mathbf{x} \)
Given matrix \(A\):
\[
A = \begin{pmatrix}
1 & 2 & 8 & -1 \\
1 & 0 & 2 & -5 \\
0 & 1 & 3 & 4 \\
-2 & 4 & 8 & 14
\end{pmatrix}
\]
The task is to find all vectors \(\mathbf{x} \in \mathbb{R}^4\) that are mapped into the zero vector by the transformation \(\mathbf{x} \rightarrow A\mathbf{x} \).
---
#### Question
Select the correct choice below and fill in the answer box within your choice.
A.
There is only one vector, which is \(\mathbf{x}\) =
\[
\begin{pmatrix}
-2 \\
-3 \\
1 \\
0 \\
\end{pmatrix}
\]
---
B. (empty box for selection)
---
C. (empty boxes for selection and entry)
\[
\begin{pmatrix}
x_1 \, (empty box) \, + \, x_3 \\
\, (empty box) + \, x_4 \, (empty box)
\end{pmatrix}
\]
---
D. (empty boxes for selection and entry)
\[
\begin{pmatrix}
x_1 \, (empty box) + \\
x_2 \, (empty box)
\end{pmatrix}
\]
---
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