Q38Comprehension2 Marks20 Nov 2022PassageLet WWW be a proper subspace of an inner product space VVV, where dim(V)=3\dim(V)=3dim(V)=3, and let PWP_WPW be the projection of VVV onto WWW.Which of the following options are true?AFor all v∈Vv\in Vv∈V, v−PW(v)v-P_W(v)v−PW(v) is orthogonal to WWW.BIf dim(W)=2\dim(W)=2dim(W)=2, then the dimension of the null space of PWP_WPW may not be 111.CThe zero vector is orthogonal to every vector of VVV.DIf v∈Wv\in Wv∈W, then PW(v)=vP_W(v)=vPW(v)=v.
