Full working is greatly appreciated, thank you! :)
Equip R5 with the Euclidean inner product (the dot product.) Let W be the subspace spanned by V1 = (1,1,0,0,0), v2 = (0,1,1,0,0), v3 = (0,0,1,1,0). Find an orthonormal basis for W. Find the element of W that is closest to (1,0,1,0,1). Find a basis for W . Find the element of W that is closest to (1,0,1,0,1).