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Let H = {A € R²×² : AT + A=0}. (i) Show that H is a subspace of R²×². (ii) Find a basis for H and determine dim(H). Let B E Rmxn (i) Define the nullspace N(B). (ii) Prove that N(B) is a subspace of Rª.

Let H = {A € R²×² : AT + A=0}. (i) Show that H is a subspace of R²×². (ii) Find a basis for H and determine dim(H). Let B E Rmxn (i) Define the nullspace N(B). (ii) Prove that N(B) is a subspace of Rª.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.1: Vector Spaces And Subspaces
Problem 34EQ: In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. 34. ,
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Let H = {A € R²×² : AT + A=0}. (i) Show that H is a subspace of R²×². (ii) Find a basis for H and determine dim(H). Let B E Rmxn (i) Define the nullspace N(B). (ii) Prove that N(B) is a subspace of Rª.
Transcribed Image Text:Let H = {A € R²×² : AT + A=0}. (i) Show that H is a subspace of R²×². (ii) Find a basis for H and determine dim(H). Let B E Rmxn (i) Define the nullspace N(B). (ii) Prove that N(B) is a subspace of Rª.
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