4 [1] 2. Is the vector 5 in the column space of matrix A = 1 0 -2 −4 4 4 5 3 -13]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Question:**
Is the vector
\[
\begin{bmatrix}
4 \\
5 \\
-2
\end{bmatrix}
\]
in the column space of matrix
\[
A = \begin{bmatrix}
1 & -4 & 5 \\
0 & 4 & 3 \\
-2 & 4 & -13
\end{bmatrix}?
\]
**Explanation:**
To determine if the given vector is in the column space of matrix \( A \), you need to see if there exists a linear combination of the columns of \( A \) that equals the vector. This involves solving the matrix equation \( A\mathbf{x} = \mathbf{b} \), where \( \mathbf{x} \) is a vector of coefficients, and \( \mathbf{b} \) is the given vector. Using row reduction or another method will help find if the solution exists.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2432691a-c29a-4a02-b85a-93b716867369%2Fa04d1e39-8c2e-4f42-bf0c-a285e02d37d9%2Fxo5kedw_processed.png&w=3840&q=75)
Transcribed Image Text:**Question:**
Is the vector
\[
\begin{bmatrix}
4 \\
5 \\
-2
\end{bmatrix}
\]
in the column space of matrix
\[
A = \begin{bmatrix}
1 & -4 & 5 \\
0 & 4 & 3 \\
-2 & 4 & -13
\end{bmatrix}?
\]
**Explanation:**
To determine if the given vector is in the column space of matrix \( A \), you need to see if there exists a linear combination of the columns of \( A \) that equals the vector. This involves solving the matrix equation \( A\mathbf{x} = \mathbf{b} \), where \( \mathbf{x} \) is a vector of coefficients, and \( \mathbf{b} \) is the given vector. Using row reduction or another method will help find if the solution exists.
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