Linear algebra p4 Find a basis of the subspace of R5 spanned by the following vectors:2-50-2111||111131-1Answer:0000

The given vectors are 2341-1, -5-2-1038, -14-256, 01111111, 00000 We have to find a basis.

Answered: Find a basis of the subspace of R5…

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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Question

Linear algebra p4

Find a basis of the subspace of R5 spanned by the following vectors:
2
-5
0
-2
11
1
||
11
11
3
1
-1
Answer:
0
0
0
0

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 1

The given vectors are

$[\begin{matrix} 2 \\ 3 \\ 4 \\ 1 \\ - 1 \end{matrix}], [\begin{matrix} - 5 \\ - 2 \\ - 10 \\ 3 \\ 8 \end{matrix}], [\begin{matrix} - 1 \\ 4 \\ - 2 \\ 5 \\ 6 \end{matrix}], [\begin{matrix} 0 \\ 11 \\ 1 \\ 11 \\ 11 \end{matrix}], [\begin{matrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{matrix}]$