Question
Determine whether the following set is a real vector space (and select what fails if it is not). The set of all upper triangular square
Determine whether the following set is a real vector space (and select what fails if it is not).
The set of all upper triangular square matrices
Closure under Addition
Closure under Scalar Multiplication
Commutativity of Addition
Associativity of Addition
Existence of Zero Vector
Existence of Additive Inverses
Multiplicative Identity
Associativity of Scalar Multiplication
Distributivity over Vector Addition
Distributivity over Scalar Addition
The set is a real vector space.
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Linear Algebra A Modern Introduction
Authors: David Poole
4th edition
1285463242, 978-1285982830, 1285982835, 978-1285463247
