Problem 2. Recall that for any subspace V of R", the orthogonal projection onto V is...
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)
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)
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
(1 point) Find the orthogonal projection of onto the subspace W of R* spanned by ņ + 9 and Otac projw() = 1
Problem 20. (3 points) Find the orthogonal projection of onto the subspace W of Rspanned by projw(v) =
A square matrix E∈Mn×n(R) is idempotent if E2=E. It is symmetric if E = tE. (a) Let V⊆Rn be a subspace of Rn, and consider the orthogonal projection projV:Rn→Rn onto V. Show that the representing matrix E = [projV]EE of proj V relative to the standard basis E of Rn is both idempotent and symmetric. (b) Let E∈Mn×n(R) be a matrix that is both idempotent and symmetric. Show that there is a subspace V⊆Rn such that E= [projV]EE. [Hint: What...
2 6 (1 point) Find the orthogonal projection of v 14 onto the subspace V of Rspanned by 6 and 8 projv(v) =
(3 points) Let W be the subspace of R spanned by the vectors 1and 5 Find the matrix A of the orthogonal projection onto W A- (3 points) Let W be the subspace of R spanned by the vectors 1and 5 Find the matrix A of the orthogonal projection onto W A-
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."
Hi, could you post solutions to the following questions. Thanks. 2. (a) Let V be a vector space on R. Give the definition of a subspace W of V 2% (b) For each of the following subsets of IR3 state whether they are subepaces of R3 or not by clearly explaining your answer. 2% 2% (c) Consider the map F : R2 → R3 defined by for any z = (zi,Z2) E R2. 3% 3% 3% 3% i. Show that...