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1. Determine whether the following subsets of the given vector spaces form a basis: a. {(1, 1, 2), (1, 2, 5), (5,3,4)} ≤ R³ over R b. {1+x,x+x²,x²+x³, x³+x¹} ≤ P4 over R where P4 is the vector space of all polynomials over R of degree at most 4

1. Determine whether the following subsets of the given vector spaces form a basis: a. {(1, 1, 2), (1, 2, 5), (5,3,4)} ≤ R³ over R b. {1+x,x+x²,x²+x³, x³+x¹} ≤ P4 over R where P4 is the vector space of all polynomials over R of degree at most 4

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 33EQ
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1. Determine whether the following subsets of the given vector spaces form a basis: a. {(1,1,2), (1, 2, 5), (5, 3, 4)} R³ over R b. {1+x,x+x²,x²+x³, x³ + x¹} ≤ P4 over R where P4 is the vector space of all polynomials over R of degree at most 4
Transcribed Image Text:1. Determine whether the following subsets of the given vector spaces form a basis: a. {(1,1,2), (1, 2, 5), (5, 3, 4)} R³ over R b. {1+x,x+x²,x²+x³, x³ + x¹} ≤ P4 over R where P4 is the vector space of all polynomials over R of degree at most 4
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