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SOLUTION6MANUAL LINEAR6ALGEBRA6AND6OPTIMIZATION6FOR6MACHINE6LEARNING 1ST6EDITION6BY6CHARU6AGGARWAL.66CHAPTERS616–611
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October 2024

2024/2025

A+
1. For6any6two6vectors6x6and6y,6which6are6each6of6length6a,6show6that6(i)6x6−6y6is6orthogonal6to6x6+6y,6and6(ii)6the6dot6product6of6x6−63y6and6x6+63y6is6negative. (i)6The6first6is6simply6x6x6y6y6using6the6distributive6property6of6matrix6multiplication.6The6dot6product6of6a6vector6with6itself6is6its6squared6length.6Since6both6vectors6are6of6the6same6length,6it6follows6that6the6result6is60.6(ii)6In6the6second6case,6one6can6use6a6similar6argument6to6show6that6the6result6is6a26−69a2,6which6is...
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