Linear Algebra 4.numbers F = R. LetW = {(a, b, c, d) | where c = a-d and a, b, c, d are real numbers }Show that W is a subspace of R¹.Consider the vector space V = R4 over the field of real

Given: Consider the vector space over the field of real numbers . Let where and are real…

Answered: 4. numbers F= R. Let W = {{a, b, c,d)|…

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

4.
numbers F = R. Let
W = {(a, b, c, d) | where c = a-d and a, b, c, d are real numbers }
Show that W is a subspace of R¹.
Consider the vector space V = R4 over the field of real

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: Solution

Given: Consider the vector space $V equals straight real numbers to the power of 4$ over the field of real numbers $F equals straight real numbers$ . Let

$W equals left curly bracket space open angle brackets a comma b comma c comma d close angle brackets space vertical line$ where $c equals a minus d$ and $a comma b comma c comma d$ are real numbers $right curly bracket$

We have To show that $W$ is a subspace of $straight real numbers to the power of 4$ .