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 + 5x29x3 = 2023. (c) The set of all vectors x = (x₁, x2, x3), satisfying 2024x₁ + X2 = (d) The set of all 3 × 3 matrices such that Ax= (e) The set of all n × n (n ¤ N) diagonal matrices. - x3 = 0. - O has a unique solution.
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 + 5x29x3 = 2023. (c) The set of all vectors x = (x₁, x2, x3), satisfying 2024x₁ + X2 = (d) The set of all 3 × 3 matrices such that Ax= (e) The set of all n × n (n ¤ N) diagonal matrices. - x3 = 0. - O has a unique solution.
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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