1. Consider the vectors a = (1,0, -2, 1), b = (0, 4, 4, 1), and c = mine the vector a-2b+2c. (5, 1, 1, 1) in R4. Deter- 2. Are the following sets vector space with standard addition and scalar multiplication? (a) V = {(x, y, z) : x² + y² + z² = 0} (b) V = {p(x) = P2: p is even that is p(x) = p(-x)} (c) V = {AЄ Mn,n; A is asymmetric that is A = -AT}
1. Consider the vectors a = (1,0, -2, 1), b = (0, 4, 4, 1), and c = mine the vector a-2b+2c. (5, 1, 1, 1) in R4. Deter- 2. Are the following sets vector space with standard addition and scalar multiplication? (a) V = {(x, y, z) : x² + y² + z² = 0} (b) V = {p(x) = P2: p is even that is p(x) = p(-x)} (c) V = {AЄ Mn,n; A is asymmetric that is A = -AT}
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:1. Consider the vectors a = (1,0, -2, 1), b = (0, 4, 4, 1), and c =
mine the vector a-2b+2c.
(5, 1, 1, 1) in R4. Deter-
2. Are the following sets vector space with standard addition and scalar multiplication?
(a) V = {(x, y, z) : x² + y² + z² = 0}
(b) V = {p(x) = P2: p is even that is p(x) = p(-x)}
(c) V = {AЄ Mn,n; A is asymmetric that is A = -AT}
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