Exercise 9

Orthogonal complement of a subspace in Cartesian form

Let

W = ⎩ ⎨ ⎧ x \in R^{4} : ⎩ ⎨ ⎧ x_{1} + x_{2} - x_{4} = 0 x_{2} + x_{3} = 0 x_{1} - x_{3} - x_{4} = 0 ⎭ ⎬ ⎫ .

Determine $dim W$ and a basis of $W^{⊥}$ .

The full solution of this exercise is in the unlocked version.