Let S be the set of matrices of the form a -a :). -b b where a and be R. The vector addition and scalar multiplication in S are the usual operations of matrix addition and scalar multiplication. i. Show that S is a vector space. ii. Find a basis and state the dimension of this space.

Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Additional Topics In Trigonometry
Section3.3: Vectors In The Plane
Problem 3ECP
icon
Related questions
Question
Let S be the set of matrices of the form
-a
a
-b b
where a and be R. The vector addition and scalar multiplication in S are the usual operations of
matrix addition and scalar multiplication.
i. Show that S is a vector space.
ii. Find a basis and state the dimension of this space.
Transcribed Image Text:Let S be the set of matrices of the form -a a -b b where a and be R. The vector addition and scalar multiplication in S are the usual operations of matrix addition and scalar multiplication. i. Show that S is a vector space. ii. Find a basis and state the dimension of this space.
Expert Solution
steps

Step by step

Solved in 4 steps with 4 images

Blurred answer
Recommended textbooks for you
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning