help with linear algebra homework Thank you!!(SEE PIC ATTACHED IN FILE){[6] , [7] , [3] , [3] , [1] , [2]}{[0] , [0] , [1] , [6] , [2] , [4]}{[0] , [0] , [0] , [0] , [3] , [6]}{[0] , [0] , [0] , [0] , [4] , [8]}{[0] , [0] , [0] , [0] , [5] , [12]} The image contains the following mathematical problem:**Question: What is the dimension of the space spanned by the following vectors?**\[\left\{\begin{bmatrix}6 \\0 \\0 \\0\end{bmatrix}, \begin{bmatrix}7 \\0 \\0 \\0\end{bmatrix}, \begin{bmatrix}3 \\1 \\0 \\0\end{bmatrix}, \begin{bmatrix}3 \\6 \\0 \\0\end{bmatrix}, \begin{bmatrix}1 \\2 \\3 \\4\end{bmatrix}, \begin{bmatrix}2 \\4 \\6 \\8\end{bmatrix}, \begin{bmatrix}5 \\3 \\4 \\5\end{bmatrix}, \begin{bmatrix}6 \\8 \\12 \\16\end{bmatrix}\right\}\]Each vector is enclosed in brackets and presented as a column vector. The problem asks for the dimension of the space these vectors span, which typically involves finding the rank of the matrix formed by these vectors.

Answered: Image /qna-images/answer/a33ee59b-9ef2-408b-b8ff-026ca86fc9e6.jpg

Answered: What is the dimension of the space…

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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help with linear algebra homework Thank you!!

(SEE PIC ATTACHED IN FILE)

{[6] , [7] , [3] , [3] , [1] , [2]}

{[0] , [0] , [1] , [6] , [2] , [4]}

{[0] , [0] , [0] , [0] , [3] , [6]}

{[0] , [0] , [0] , [0] , [4] , [8]}

{[0] , [0] , [0] , [0] , [5] , [12]}

The image contains the following mathematical problem:

**Question: What is the dimension of the space spanned by the following vectors?**

\[
\left\{
\begin{bmatrix}
6 \\
0 \\
0 \\
0
\end{bmatrix},
\begin{bmatrix}
7 \\
0 \\
0 \\
0
\end{bmatrix},
\begin{bmatrix}
3 \\
1 \\
0 \\
0
\end{bmatrix},
\begin{bmatrix}
3 \\
6 \\
0 \\
0
\end{bmatrix},
\begin{bmatrix}
1 \\
2 \\
3 \\
4
\end{bmatrix},
\begin{bmatrix}
2 \\
4 \\
6 \\
8
\end{bmatrix},
\begin{bmatrix}
5 \\
3 \\
4 \\
5
\end{bmatrix},
\begin{bmatrix}
6 \\
8 \\
12 \\
16
\end{bmatrix}
\right\}
\]

Each vector is enclosed in brackets and presented as a column vector. The problem asks for the dimension of the space these vectors span, which typically involves finding the rank of the matrix formed by these vectors.

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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