Exercise 1. Answer True or False. i) If u, v are two vectors in the inner product space V such that ||u + v|| = ||| + ||v||, then (u, v)

Extracted text: Exercise 1. Answer True or False. i) If u, v are two vectors in the inner product space V such that ||u + v|| = ||| + ||v||, then (u, v) < 0.="" %3d="" ii)="" if="" t="" :="" v="" →="" v="" is="" an="" operator="" on="" the="" inner="" product="" space="" v="" such="" that="" ||t(u)||="">< 2||||="" for="" all="" u="" e="" v,="" then="" |a="">< 2,="" for="" all="" eigenvalues="" a="" of="" t.="" iii)="" suppose="" u,="" v="" are="" two="" non="" zero="" vectors="" in="" a="" real="" inner="" product="" space="" v,="" if="" ||u||="||||." then="" u="" +="" v="" is="" orthogonal="" to="" u-="" v.="" iv)="" consider="" r?="" with="" its="" euclidean="" inner="" product.="" there="" exists="" three="" non-zero="" vectors="" in="" r?,="" which="" are="" mutually="" orthogonal.="" v)="" the="" function="" that="" takes="" (71,="" x2),="" (y1,="" y2)="" e="" r²="" to="" r142="" +="" 12y1="" is="" an="" inner="" product="" on="">