et V denote the set of 2 × 2 invertible matrices with real entries. If A, B ∈ V and α ∈ R, define vector-addition (A ⊕ B) and scalar-multiplication (α*A) by A ⊕ B = AB (matrix product), and α*A = αA. Determine whether V is a vector space. Justify your answer
et V denote the set of 2 × 2 invertible matrices with real entries. If A, B ∈ V and α ∈ R, define vector-addition (A ⊕ B) and scalar-multiplication (α*A) by A ⊕ B = AB (matrix product), and α*A = αA. Determine whether V is a vector space. Justify your answer
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let V denote the set of 2 × 2 invertible matrices with real entries. If A, B ∈ V and
α ∈ R, define vector-addition (A ⊕ B) and scalar-multiplication (α*A) by
A ⊕ B = AB (matrix product),
and α*A = αA.
Determine whether V is a vector space. Justify your answer
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