The best approximation to by elements of a subspace W is given by the vector −projW(). 2. If an ×p matrix has orthonormal columns, then T= for all in ℝ. 3. If W is a subspace of ℝ and if is in both W and W⊥, then must be the zero vector. 4. If =1+2, where 1 is in a subspace W and 2 is in W⊥, then 1 must be the orthogonal projection of onto W. 5. Let 1,2,…, be an orthonormal basis of a vector space . In the Orthogonal Decomposition Theorem, each term =⟨,1⟩1+…+⟨,⟩ is itself an orthogonal projection of onto a subspace of .

Consider the following geometry problems in 3-space enter t or f depending on whether the statement is true or false. (you must enter t or f -- true and false will not work.) f equation editorequation editor 1. a plane and a line either intersect or are parallel t equation editorequation editor 2. two planes parallel to a third plane are parallel f equation editorequation editor 3. two lines either intersect or are parallel f equation editorequation editor 4. two planes orthogonal to a third plane are parallel f equation editorequation editor 5. two planes orthogonal to a line are parallel f equation editorequation editor 6. two planes either intersect or are parallel f equation editorequation editor 7. two lines orthogonal to a third line are parallel t equation editorequation editor 8. two lines parallel to a third line are parallel t equation editorequation editor 9. two planes parallel to a line are parallel f equation editorequation editor 10. two lines parallel to a plane are parallel f equation editorequation editor 11. two lines orthogonal to a plane are parallel