MAT2611 ASSIGNMENT 2 FULL SOLUTIONS 2024 UNISA
,MAT2611 ASSIGNMENT 2 FULL SOLUTIONS 2024 UNISA
, MAT2611 ASSIGNMENT 2 FULL SOLUTIONS 2024 UNISA
SOLUTION
Problem 5
We shall use the vector space axioms, VS1 – VS10, below to solve problems.
(1) Let u = (x, 0), v = (y, 0) and w = (z, 0) where u, v ∈ U
VS1. u + v = (x, 0) + (y, 0) = (x+y, 0) ∈ 𝑈 .
Hence u + v ∈ V for all u, v ∈ U
Thus VS1 holds.
VS2. u + v = (x, 0) + (y, 0) = (x+y, 0)
= (y + x, 0 )
,MAT2611 ASSIGNMENT 2 FULL SOLUTIONS 2024 UNISA
, MAT2611 ASSIGNMENT 2 FULL SOLUTIONS 2024 UNISA
SOLUTION
Problem 5
We shall use the vector space axioms, VS1 – VS10, below to solve problems.
(1) Let u = (x, 0), v = (y, 0) and w = (z, 0) where u, v ∈ U
VS1. u + v = (x, 0) + (y, 0) = (x+y, 0) ∈ 𝑈 .
Hence u + v ∈ V for all u, v ∈ U
Thus VS1 holds.
VS2. u + v = (x, 0) + (y, 0) = (x+y, 0)
= (y + x, 0 )
