Let {a1, a2,..., an} be a basis of a vector space V, n > 2. Show that {a1, a1 + a2,...,ɑj + az + ·… · + an} is also a basis of V. Is the set {a1 + a2, a2 +a3, . . . , On=1 + am, an t ai} a basis for V too? How about the converse?

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.5: Basis And Dimension
Problem 65E: Find a basis for the vector space of all 33 diagonal matrices. What is the dimension of this vector...
icon
Related questions
Topic Video
Question

pls help me 

Let {a1, a2,..., an} be a basis of a vector space V, n > 2. Show that
{a1, a1 + a2,...,ɑj + az + · … · + an} is also a basis of V. Is the set
{a1 + a2, a2 +a3, . . . , ɑn=1 + an, an t ai}
a basis for V too? How about the converse?
Transcribed Image Text:Let {a1, a2,..., an} be a basis of a vector space V, n > 2. Show that {a1, a1 + a2,...,ɑj + az + · … · + an} is also a basis of V. Is the set {a1 + a2, a2 +a3, . . . , ɑn=1 + an, an t ai} a basis for V too? How about the converse?
Expert Solution
steps

Step by step

Solved in 4 steps with 3 images

Blurred answer
Knowledge Booster
Algebraic Operations
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
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