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Q Desciibe if the twea surspaces U=span(V) ar V=span(V) spanned hy the twea seneets and arthegand complementa) V={[[1],[-1]]} ment with respeect to R^(3) ?If V and V are orthoganal If inner probuet of rectors of V and V is 0{:[{: < [[1],[-1],[1]][[1],[1],[0]]:)=1+(-1)+0=1-1=0],[(:[[1],[-1],[1]],[[-1],[-1],[-1]]:)=-1+1-1=-1!=0]:}hence U&V are nat orthegonal orthegonal subspaer falseJulo vectors U and V are orthegonel complement{:[" if "R^(3)=u+v],[" and "u nn v={0}],[u nn v={0}],[u+v=R^(3)]:}If the vectors {[[1],[-1],[1]],[[1],[1],[0]]*[[-1],[-1],[-1]]} areLinearly Independent.Let alpha,beta,gamma be thee constants s't'{:[alpha[[1],[-1],[2]]+beta[[1],[1],[0]]+gamma[[-1],[-1],[-2]]=[[0],[0],[0]]],[[[alpha+beta-gamma],[-alpha+beta-gamma],[alpha-gamma]]=[[0],[0],[0]]],[alpha-gamma=0],[alpha=gamma],[alpha+beta-alpha=0],[=>quad beta=0],[-alpha+0-alpha=0],[-2^(alpha)=0],[=>alpha=0]:}{:[alpha=gamma=0],[=>alpha=beta=gamma=0]:}hemis u and v ase ot haganel cimplaments'b) V={[[0],[1],[-2]},v={[[0],[-2],[2]]0[[-2],[-1],[-1]]}:}for oxthaganel surspace(:[[0],[1],[-2]],[[0],[-1],[2]]:)=0-1-1=-2!=0hance U & V are not orthegonel{:[{[[0],[1],[-1]],[[0],[-1],[1]],[[-1],[-1],[-2]]}],[alpha[[0],[1],[-1]]+beta[[0],[-1],[2]]+gamma[[-1],[-2],[-2]]=[[0],[0],[0]]],[=[[alpha-beta-gamma],[-alpha+beta-gamma]]=[[0],[0],[0]]],[gamma=0]:}{:[gamma=0],[alpha-beta=0],[-alpha+beta=0],[alpha=beta=>alpha" and "beta" que not aleerss "]:}{:[[[1],[0],[0]]=],[[[1],[0],[0]]epsiR^(3)]:}but [[2],[0],[0]] conmat be written as theLincea corpination of vectors of U and V lence U and v axe not othegonel complements'othen oral sutspac ... See the full answer