Question:

Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector orthogonal to W. y = 4 u₁ = 1 u₂ = -1 u₃ = -1 2 1

Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector orthogonal to W.
y = 4       u₁ = 1        u₂ = -1         u₃ =  -1
      2               1                 3                    0
      2               0                 1                    1
     -1              1                -2                    1

Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector orthogonal to W. y = 4 u₁ = 1 u₂ = -1 u₃ = -1 2 1 3 0 2 0 1 1 -1 1 -2 1