Let V be the set of all real n x n matrices. It can be shown that V is a vector space over R with respect to standard/usual addition of matrices and scalar multiplication. Now suppose that L is the set of all real n x n lower triangular matrices. Is La subspace of V? Give a very short argument that supports your claim.
Let V be the set of all real n x n matrices. It can be shown that V is a vector space over R with respect to standard/usual addition of matrices and scalar multiplication. Now suppose that L is the set of all real n x n lower triangular matrices. Is La subspace of V? Give a very short argument that supports your claim.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.5: Subspaces, Basis, Dimension, And Rank
Problem 4EQ: In Exercises 1-4, let S be the collection of vectors in [xy]in2 that satisfy the given property. In...
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