[Solution Library] Equip R^4 with the Euclidean inner product (the dot product.) Let W be the subspace spanned by (1,0,1,1),(-1,1,0,1), \text and (1,-1,1,0)
Question: Equip \(\mathbb{R}^{4}\) with the Euclidean inner product (the dot product.) Let \(W\) be the subspace spanned by
\[(1,0,1,1),(-1,1,0,1), \text { and }(1,-1,1,0)\]- Find an orthonormal basis for \(W\).
- Find the element of \(W\) that is closest to \((1,1,1,1)\).
- Find a basis for \(W^{\perp}\).
- Find the element of \(W\) that is closest to \((0,8,8,-8)\).
- Find the matrix of the projection \(P_{W}\) with respect to the standard basis of \(\mathbb{R}^{4}\).
Deliverable: Word Document 
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