4.4.3. Find the orthogonal projection of v (1,2,-1,2) onto the following subspaces: 12 20 1-1 01 ...
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 [2,1,0,-]. Make sure you are working with an orthonormal basis for u span(u, u2 before you use the usual projection formula. 2. Consider R with the weighted inner product = [wn, u, tva, teal"). [ruh, t', talT and w Find the orthogonal projection of...
Find the orthogonal projection of v=[1 8 9] onto the subspace V of R^3 spanned by [4 2 1] and [6 1 2] (1 point) Find the orthogonal projection of v= onto the subspace V of R3 spanned by 2 6 and 1 2 9 projv(v)
(1 point) Find the orthogonal projection of V = onto the subspace V of R4 spanned by X1 = and X2 = 3/2 projv(v) = -39/2
2 6 (1 point) Find the orthogonal projection of v 14 onto the subspace V of Rspanned by 6 and 8 projv(v) =
Find the orthogonal projection of v = |8,-5,-5| onto the subspace W of R^3 spanned by |7,-6,1| and |0,-5,-30|. (1 point) Find the orthogonal projection of -5 onto the subspace W of R3 spanned by 7 an 30 projw (V)
28 -? (1 point) Find the orthogonal projection of 14 onto the subspace V of R3 spanned by 32and y- 7 -2 (Note that the two vectors x and y are orthogonal to each other.) projv(V)-
Problem 2. Recall that for any subspace V of R", the orthogonal projection onto V is the map projy : RM → Rn given by projy() = il for all i ER", where Ill is the unique element in V such that i-le Vt. For any vector space W, a linear transformation T: W W is called a projection if ToT=T. In each of (a) - (d) below, determine whether the given statement regarding projections is true or false, and...
(1 point) Find the orthogonal projection of -1 -5 V = 9 -11 onto the subspace V of R4 spanned by -4 -2 -4. -5 X1 = and X2 1 -28 -4 0 projv(v)
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."
(1 point) Find the orthogonal projection of 0 0 -7 1 V = 4 onto the subspace V of R4 spanned by 1 -1 -1 -1 -1 -1 -1 1 , and 7 1 -1 1 proj,(v) =