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Linear Algebra Homework 8: Subspaces Intersection and Union, Assignments of Linear Algebra

Colgate UniversityLinear Algebra

The eighth week homework for math 214 linear algebra course. The assignment covers the concepts of subspaces intersection and union. Students are required to prove that the intersection of two subspaces is a subspace and provide an example in r2 to show that the union of two subspaces is not a subspace in general.

Typology: Assignments

Pre 2010

Uploaded on 08/17/2009

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MATH 214
Linear Algebra
Week 8
Homework (Due 3/24)
Date Section Assignment
3/7 4.1 1, 2, 6, 9, 12, 21, 24, 24, 26, 28, 31
Bonus Question
1. Let Hand Kbe subspaces of a vector space V. The intersection of Hand K, written as
H∩K, is the set of vectors that belong to both Hand K. Show that H∩Kis a subspace
of V. Give an example in R2to show that the union of two subspaces is not, in general, a
subspace.
1

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MATH 214

Linear Algebra

Week 8

Homework (Due 3/24)

Date Section Assignment 3/7 4.1 1, 2, 6, 9, 12, 21, 24, 24, 26, 28, 31

Bonus Question

  1. Let H and K be subspaces of a vector space V. The intersection of H and K, written as H ∩ K, is the set of vectors that belong to both H and K. Show that H ∩ K is a subspace of V. Give an example in R^2 to show that the union of two subspaces is not, in general, a subspace.