2 Determine whether the vectors form a basis for R*. (You may use any relevant theorem that we have covered; remember that it must be cited and you must explain why the theorem applies.)
2 Determine whether the vectors form a basis for R*. (You may use any relevant theorem that we have covered; remember that it must be cited and you must explain why the theorem applies.)
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
![**Problem Statement:**
Determine whether the vectors
\[
\left\{
\begin{bmatrix}
1 \\ -1 \\ 3 \\ -1
\end{bmatrix},
\begin{bmatrix}
3 \\ 1 \\ 2 \\ 0
\end{bmatrix},
\begin{bmatrix}
1 \\ 5 \\ 1 \\ 2
\end{bmatrix},
\begin{bmatrix}
1 \\ 2 \\ 4 \\ 2
\end{bmatrix}
\right\}
\]
form a basis for \(\mathbb{R}^4\). (You may use any relevant theorem that we have covered; remember that it must be cited and you must explain why the theorem applies.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fffc06da2-7bd8-42a3-b8a1-3f8b831a8034%2F49ce9b69-1d70-4e13-bcd7-6e04f1086061%2Fsa5310s_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Determine whether the vectors
\[
\left\{
\begin{bmatrix}
1 \\ -1 \\ 3 \\ -1
\end{bmatrix},
\begin{bmatrix}
3 \\ 1 \\ 2 \\ 0
\end{bmatrix},
\begin{bmatrix}
1 \\ 5 \\ 1 \\ 2
\end{bmatrix},
\begin{bmatrix}
1 \\ 2 \\ 4 \\ 2
\end{bmatrix}
\right\}
\]
form a basis for \(\mathbb{R}^4\). (You may use any relevant theorem that we have covered; remember that it must be cited and you must explain why the theorem applies.)
Expert Solution
Step 1
A basis for a subspace S of Rn is a set of vectors in S that is linearly independent and is maximal with this property (that is, adding any other vector in S to this subset makes the resulting set linearly dependent).
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