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…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 39RE

See similar textbooks

Related questions

Question

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.

Expert Solution

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

What is the dimension of the space spanned by 7. 3 3 1 6. 6 4 8. 0. 12