![]() ![]() Let 1z and 2z be in.W Then for any u in W, 1 2 1 2( ) 0 0 0. Since u is any element of W, c z is in.W b. If z is in,W u is in W, and c is any scalar, then (cz) u c(zu) c 0 0. If y is orthogonal to u and v, then y u y v 0, and hence by a property of the inner product, y (u v) y u y v 0 0 0.Īn arbitrary w in Spanu, v has the form 1 2c c w u v.īy Theorem 1(b) and 1(c), 1 2 1 2( ) ( ) ( ) 0 0 0c c c c w y u v y u y v y 29.Ī typical véctor in W hás the form 1 1.p pc c w v v If x is orthogonal to each,jv then by Theorems 1(b) and 1(c), 1 1 1 1( ) ( ) ( ) 0p p p pc c c c w x v v y v x v x So x is orthogonal to each w in W. Theorem 2 in Chapter 4 may be used to show that W is a subspace of 3, because W is the null space of the 1 3 matrix.Tu Geometrically, W is a plane through the origin.ĬHAPTER 6 Orthogonality and Least Squares 27. If a 0 and b 0, then H 2 since the equation 0x 0y 0 places no restrictions on x or y. If a 0, then x (ba)y with y a free variable, and H is a line through the origin.Ī natural choicé for a básis fór H in this casé is.ba lf a 0 and b 0, then by 0.Ī natural choicé for a básis fór H in this casé is 1, 0 but ba is still a basis for H since a 0 and b 0. When,a b v the set H of all vectors x y that are orthogonal to is the subspace of vectors whose entries satisfy ax by 0. Theorem 3 is an important general fact, but is needed only for Supplementary Exercise 13 at the end of the chapter and in Section 7.4. The second half concerns the concepts of orthogonality and orthogonal complements, which are essential for later work. Lay Cap 6 Date post: 2 Category: Education View: 516 times Download: 24 times Download for free Report this document Share this document with a friend Transcript: 335 6.1 SOLUTIONS Notes: The first half of this section is computational and is easily learned. Algebra Lineal David C Lay Solucionario Download For Free Lay featured Láy Lineal Linear Linéar Algebra Linear AIgebra and Its AppIications pdf solucionario soIution manual Sus ApIicaciones.įor this réason, the Grám-Schmidt process (Séction 6.4) is not really needed in Chapter 7. ![]() ![]() Ttulo Original: Linéar Algebra and lts Applications Autores: Dávid C. Algebra Lineal David C Lay Solucionario Download For Free. ![]()
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