Determine the dimensions of the following subspaces of R* a) All vectors of the form (a, b, c, d), where d = a +b y c = a - b. b) All vectors of the form (a, b, c, d), where a = b =c = d.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 54CR: Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector...
icon
Related questions
Question

Which of the following are vector subspaces of R4?

  1. all vectors of the form (a, b, c), where b = a + c?
  2. all vectors of the form (a, b, c), where b = a + c + 1?

Note: In the image the problem is described more clearly, do not skip any step and solve the two parts a and b.

Determine the dimensions of the following subspaces of R*
a) All vectors of the form (a, b, c, d), where d = a + b y c = a - b.
b) All vectors of the form (a, b, c, d), where a = b = c = d.
Transcribed Image Text:Determine the dimensions of the following subspaces of R* a) All vectors of the form (a, b, c, d), where d = a + b y c = a - b. b) All vectors of the form (a, b, c, d), where a = b = c = d.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Vector Space
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage