4. Let F = R, V := R, X, Y be the x-axis and y-axis, respectively,...

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4. Let F = R, V := R², X, Y be the x-axis and y-axis, respectively, and D := {(r,r): re R²)} be the diagonal. Replace the question marks below to describe explicit formulas for the following projections: (a) Px/y(x,y)= (?,?). (b) Px/D(x, y) = (?, ?). 5. V be an F-vector space and let U, W CV be subspaces such that V = U + W. Prove: (a) Pu/w is a linear operator. (b) ker(Pu/w) W and im(Pu/w) = U. (c) Pu/wlu = idu, where recall that Pu/wly denotes the restriction of the function Pu/w to the set U. (d) Pu/w is idempotent, i.e. P/w = Pu/w, where Pu/w - Pu/w o Pu/w. 4. Let F = R, V := R², X, Y be the x-axis and y-axis, respectively, and D := {(r,r): re R²)} be the diagonal. Replace the question marks below to describe explicit formulas for the following projections: (a) Px/y(x,y)= (?,?). (b) Px/D(x, y) = (?, ?). 5. V be an F-vector space and let U, W CV be subspaces such that V = U + W. Prove: (a) Pu/w is a linear operator. (b) ker(Pu/w) W and im(Pu/w) = U. (c) Pu/wlu = idu, where recall that Pu/wly denotes the restriction of the function Pu/w to the set U. (d) Pu/w is idempotent, i.e. P/w = Pu/w, where Pu/w - Pu/w o Pu/w.

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a The formula for the projection Pxyx y onto the xaxis is x 0 b The formula for the projection Pxpx ... View the full answer