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Exercise 20 Let fr,y} be an orthonormal basis of a two-dimensional subspace S of R and T A= xx SL (i) Show that N(A (ii) Sho

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Ourston (xtivειSι 2ο . ditf, b orthonovmol bosis two diminsional Subsnac S d R ond A-xxT yyT (il Shous thatNCA)= S. (ii) ShosAmtw fv od tx,Y3 det S 3poa ov thonovmmal Subset A xxt yyt Claim ni(A olet2 (A1 A Cxxt yyt )2 = o A2 xxt 2 +- CytY (xt2) oudyono 2F S xtztz O A2 0 2 F A (A) N CA) S mat dim Rn- dim (A) dimN (A) dim s 11 Hονe By Ronk Nutlity n2 dim |R^ - dimriA) olimBiitavly yis giv viutov d A with givu volue オ=yty Rom is 2 A A = tx + Cxtx) x o CYx = o A with qivu Volue AzxtY 2 is qivn vi

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