Which of the following are vector spaces? Justify your answer. (a) The set of all polynomials of degree 3. = 2023. (b) The set of all vectors x = (x1, x2, x3), satisfying 3x₁ + 5x2 – 9x3 (c) The set of all vectors x = : (x1, x2, x3), satisfying 2024x₁ + x2 − x3 = 0. (d) The set of all 3 × 3 matrices such that Ax 0 has a unique solution. (e) The set of all n × n (n = N) diagonal matrices. =
Which of the following are vector spaces? Justify your answer. (a) The set of all polynomials of degree 3. = 2023. (b) The set of all vectors x = (x1, x2, x3), satisfying 3x₁ + 5x2 – 9x3 (c) The set of all vectors x = : (x1, x2, x3), satisfying 2024x₁ + x2 − x3 = 0. (d) The set of all 3 × 3 matrices such that Ax 0 has a unique solution. (e) The set of all n × n (n = N) diagonal matrices. =
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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Transcribed Image Text:**Which of the following are vector spaces? Justify your answer.**
(a) The set of all polynomials of degree 3.
(b) The set of all vectors **x** = (x₁, x₂, x₃), satisfying 3x₁ + 5x₂ − 9x₃ = 2023.
(c) The set of all vectors **x** = (x₁, x₂, x₃), satisfying 2024x₁ + x₂ − x₃ = 0.
(d) The set of all 3 × 3 matrices such that A**x** = 0 has a unique solution.
(e) The set of all n × n (n ∈ ℕ) diagonal matrices.
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