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MAT2611 ASSIGNMENT 8 SEMESTER 1 2022
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- University Of South Africa (Unisa)
This document contains MAT2611 ASSIGNMENT 8 SEMESTER 1 2022 solutions. Explanations and clear calculations are provided
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JC TUTORIALSMAT2611
ASSIGNMENT 8
SEMESTER 1
2022
, Problem 27:
Solution:
𝐿𝑒𝑡𝑠 𝑐ℎ𝑜𝑜𝑠𝑒 (𝑥1 , 𝑥2 , 𝑥3 ) = (0,1,0) , 𝑖𝑡 𝑓𝑜𝑙𝑙𝑜𝑤𝑠 𝑡ℎ𝑎𝑡
((𝑥1 , 𝑥2 , 𝑥3 )(𝑥1 , 𝑥2 , 𝑥3 )) = (𝑥1 )2 + (𝑥3 )2
𝑆𝑖𝑛𝑐𝑒 (𝑥1 , 𝑥2 , 𝑥3 ) = (0,1,0) 𝑡ℎ𝑒𝑛 𝑥1 = 0, 𝑥2 = 1, 𝑥3 = 0
((𝑥1 , 𝑥2 , 𝑥3 )(𝑥1 , 𝑥2 , 𝑥3 )) = (𝑥1 )2 + (𝑥3 )2
= (0)2 + (0)2
=0
𝑆𝑖𝑛𝑐𝑒 ((𝑥1 , 𝑥2 , 𝑥3 )(𝑥1 , 𝑥2 , 𝑥3 )) = 0 𝑤ℎ𝑒𝑛 (𝑥1 , 𝑥2 , 𝑥3 ) = (0,1,0) ≠ 0
𝐵𝑦 𝑑𝑒𝑓𝑖𝑛𝑖𝑡𝑖𝑜𝑛:
𝐼𝑛 𝑐𝑜𝑛𝑐𝑙𝑢𝑠𝑖𝑜𝑛 𝑡ℎ𝑒 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝑖𝑠 𝑛𝑜𝑡 𝑎 𝑖𝑛𝑛𝑒𝑟 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑏𝑒𝑐𝑎𝑢𝑠𝑒 𝑖𝑡 𝑑𝑜𝑒𝑠 𝑛𝑜𝑡 𝑠𝑎𝑡𝑖𝑠𝑓𝑦 𝑑𝑒𝑓𝑖𝑛𝑖𝑡𝑒𝑛𝑒𝑠𝑠.
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