Determine if y is in the subspace of R4 spanned by the columns of A. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The vector y is in the subspace spanned by the columns of A because y can be written as a linear combination of these columns as follows. -3 -6 -8 -8 -5 4 9 29 -12 23 (Type integers or simplified fractions.) OB. The vector y is not in the subspace spanned by the columns of A. y= 6 -6 0 + 6 -9 -7 y = -3 -8 6 -6 A= 9-6-8 29 6-5 4 -12 -9 23-1-7
Determine if y is in the subspace of R4 spanned by the columns of A. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The vector y is in the subspace spanned by the columns of A because y can be written as a linear combination of these columns as follows. -3 -6 -8 -8 -5 4 9 29 -12 23 (Type integers or simplified fractions.) OB. The vector y is not in the subspace spanned by the columns of A. y= 6 -6 0 + 6 -9 -7 y = -3 -8 6 -6 A= 9-6-8 29 6-5 4 -12 -9 23-1-7
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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![The task is to determine if the vector \( y \) is in the subspace of \( \mathbb{R}^4 \) spanned by the columns of matrix \( A \).
Given:
\[ y = \begin{bmatrix} -3 \\ -8 \\ 6 \\ -6 \end{bmatrix}, \quad A = \begin{bmatrix} 9 & -6 & -8 \\ 29 & 6 & -5 \\ -12 & -9 & 4 \\ 23 & -1 & -7 \end{bmatrix} \]
Select the correct choice and, if necessary, fill in the answer boxes to complete your choice.
Choices:
- **Option A**: The vector \( y \) is in the subspace spanned by the columns of \( A \) because \( y \) can be written as a linear combination of these columns as follows:
\[
\begin{bmatrix}
9 & -6 & -8 \\
29 & 6 & -5 \\
-12 & -9 & 4 \\
23 & -1 & -7
\end{bmatrix}
\begin{bmatrix}
c_1 \\
c_2 \\
c_3
\end{bmatrix}
=
\begin{bmatrix}
-3 \\
-8 \\
6 \\
-6
\end{bmatrix}
\]
(Type integers or simplified fractions.)
- **Option B**: The vector \( y \) is not in the subspace spanned by the columns of \( A \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F08f6f3ae-62d0-4ecf-a7d1-a70a7054db3c%2F23be8998-63ae-47e7-997d-8cebc70140a8%2F6bq6zjw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The task is to determine if the vector \( y \) is in the subspace of \( \mathbb{R}^4 \) spanned by the columns of matrix \( A \).
Given:
\[ y = \begin{bmatrix} -3 \\ -8 \\ 6 \\ -6 \end{bmatrix}, \quad A = \begin{bmatrix} 9 & -6 & -8 \\ 29 & 6 & -5 \\ -12 & -9 & 4 \\ 23 & -1 & -7 \end{bmatrix} \]
Select the correct choice and, if necessary, fill in the answer boxes to complete your choice.
Choices:
- **Option A**: The vector \( y \) is in the subspace spanned by the columns of \( A \) because \( y \) can be written as a linear combination of these columns as follows:
\[
\begin{bmatrix}
9 & -6 & -8 \\
29 & 6 & -5 \\
-12 & -9 & 4 \\
23 & -1 & -7
\end{bmatrix}
\begin{bmatrix}
c_1 \\
c_2 \\
c_3
\end{bmatrix}
=
\begin{bmatrix}
-3 \\
-8 \\
6 \\
-6
\end{bmatrix}
\]
(Type integers or simplified fractions.)
- **Option B**: The vector \( y \) is not in the subspace spanned by the columns of \( A \).
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