Question (1 point) Decide if the two subspaces U = span(V) and V = span(V) spanned by the two subsets V and V of vectors in R3 below are (1) orthogonal to one another and (2) orthogonal complements of one another with respect to R3. Answer by entering 'true' or 'false'. Orthogonal Subspaces? Orthogonal Complements? U = Orthogonal Subspaces? Orthogonal Complements? »-0-00 ) -{{ 3-06 - 0 v- ] -- {}-06 V = V = Orthogonal Subspaces? Orthogonal Complements? 14 V = -3 4 Orthogonal Subspaces? Orthogonal Complements? V = Orthogonal Subspaces? Orthogonal Complements?

NTBXKI The Asker · Advanced Mathematics

Transcribed Image Text: (1 point) Decide if the two subspaces U = span(V) and V = span(V) spanned by the two subsets V and V of vectors in R3 below are (1) orthogonal to one another and (2) orthogonal complements of one another with respect to R3. Answer by entering 'true' or 'false'. Orthogonal Subspaces? Orthogonal Complements? U = Orthogonal Subspaces? Orthogonal Complements? »-0-00 ) -{{ 3-06 - 0 v- ] -- {}-06 V = V = Orthogonal Subspaces? Orthogonal Complements? 14 V = -3 4 Orthogonal Subspaces? Orthogonal Complements? V = Orthogonal Subspaces? Orthogonal Complements?

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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