Unformatted text preview: 1) The normal equations are A T A ˆ x = A T b , so you substitute into that, and get ± 611 6 ² ˆ x = ± 2025 ² I intended for you to multiply out A T A and A T b , but gave full credit without that. I gave 2 points extra credit if you did so. 2) In R n , we compute the norm of a vector from  x  = ( x T x ) 1 / 2 . In an inner product space, we use h x,x i instead. ( R 1 ( x + 1) 2 dx ) 1 / 2 = p 7 / 3. 3a) [This was HW, and we also did it in class]. The part about Ax ∈ R ( A ) is from basic deﬁnitions (see pages 3637). And x ∈ N ( A T A ) means A T A x = which means A x ∈ N ( A T ). By the main thm (5.2.1), these show that A x ∈ S ∩ S ⊥ = { } (see Remark 1 on page 227). 3b) See the text. You should really include the paragraph above Theorem 5.2.1, too, though I wasn’t very strict about that this time. 1...
View
Full Document
 Spring '09
 JULIANEDWARDS
 Normal Distribution, Trigraph, ax, Linear least squares, normal equations, Prof. S. Hudson

Click to edit the document details