2. Consider R with the weighted inner product = [wn, u, tva, teal"). [ruh, t', talT and w Find the orthogonal projection of w = [1, 2,-1,2]T onto the span of ui-|1,-1, 2, 5]T and u2 [2,1,...
4.4.3. Find the orthogonal projection of v (1,2,-1,2) onto the following subspaces: 12 20 1-1 01 (a) the span of2 (b) the ma of the aris b3(0) the kernel of the matrix-2 Warning. Make sure you have an orthogonal basis before applying formula (4.42)! ; (d) the subspace orthogonal to a (1,-1,0,1) 4.4.3. Find the orthogonal projection of v (1,2,-1,2) onto the following subspaces: 12 20 1-1 01 (a) the span of2 (b) the ma of the aris b3(0) the...
(1 point) Consider the complex inner product space C with the usual inner product Let -4i 4i and let w = span(vi,V2). (a) Compute the following inner products: (v.vi)- 2 (Vi, V2-12 (2. V)12 (b) Apply the Gram-Schmidt procedure to Vi and v2 to find an orthogonal basis (ui,u2l for W , u2=1112
Let R2 have the Euclidean inner product. (a) Find wi, the orthogonal projection of u onto the line spanned by the vector v. (b) Find W2, the component of u orthogonal to the line spanned by the vector v, and confirm that this component is orthogonal to the line. u =(1,-1); v = (3,1) (a) wi = Click here to enter or edit your answer (0,0) Click here to enter or edit your answer (b) 2 = W2 orthogonal to...
2. Let M,, be equipped with the standard inner product. Prove. u is orthogonal W-span w,w,w) 3 -1 note: You must use some of the axioms in the definition of an inner product 2. Let M,, be equipped with the standard inner product. Prove. u is orthogonal W-span w,w,w) 3 -1 note: You must use some of the axioms in the definition of an inner product
Find the orthogonal projection of v ⃗=(-7, -9, -6, 10) onto he subspace W spanned by{(-2, -2, -3, 4),(-3, -1, 4, -2)}. I posted this question to my instructor: "I have tried to use the calculation (v*u1)/(u1*u1)+(v*u2)/(u2*u2) and my result is [-223/55 -823/165 -1658/165 1954/165]" and got this reply: "You can only use the dot product formula if the basis vectors are orthogonal. In this case, they aren't."
9 -4 0 0 A4 5 2 0 0 0 1 2 and consider the vector space R4 with the inner product given by v, w)Aw. Let 0 0 -2 and let W span(Vi, V2, V3 ). In this problem, you will apply the Gram-Schmidt procedure to vi, v2, v3 to find an orthogonal basis (u, u2, u31 for W (with respect to the above inner product). b) Compute the following inner products. (v2, u1) - Then u2 =Y2__v2.ul) ui,...
Let Ps have the inner product given by evaluation at -2, -1, 1, and 2. Let po(t)-1. P,()-t, and p20)- a. Compute the orthogonal projection of p2 onto the subspace spanned by Po and P1 b. Find a polynomial q that is orthogonal to Po and p,, such that Po P is an orthogonal basis for Span(Po P1, P2). Scale the polynomial q so that its vector of values at a2(Simplify your answer.) Let Ps have the inner product given...
how to do number 16 16) (6pts) Find the projection of ü onto w. a) Find ui --Son 347 2 25 26 b) Find 펄 orthogonal to in such that iiitül ü 2 Page Score Check ( 13 For problems on this page, use the vectors described graphically here. Your work should include correct vector notation of u, i,and w 13) What is (w+u) v E xplat 3 U=(2、1) w (3, .. 4) 14) Find the cxact magnitudes of i,...
Problem 5. (1 point) Find the orthogonal projection of -2 -6 onto the subspace W of R spanned by 4 -2 -7 projw (v) preview answers
-4 -2 -5 (1 point) Find the orthogonal projection of ū onto the subspace W spanned by -26 11 -35 -3 -3 2 3 -219 -806 projw(Ū) = -17 -950