Question

Find the orthogonal projection of v =[12 -3 9 -16] onto the subspace W spanned by {[-2 4 1 -1],[-4 0 -1 -4],[-4 1 -3 4]}

Answer #1

Find the orthogonal projection of v=[−2,10,−16,−19] onto the
subspace W spanned by [-4,0,-2,1],[-4,-2,5,1],[3,-1,-3,4]

Find the orthogonal projection of u onto the
subspace of R4 spanned by the vectors
v1, v2 and
v3.
u = (3, 4, 2, 4) ;
v1 = (3, 2, 3, 0),
v2 = (-8, 3, 6, 3),
v3 = (6, 3, -8, 3)
Let (x, y, z, w) denote the
orthogonal projection of u onto the given
subspace. Then, the components of the target orthogonal projection
are

Find the orthogonal projection of v⃗ =⎢4,−11,−36,9⎤ onto the
subspace W spanned by ⎢0,0,−5,−2| , |−4,2,5,−5⎢ , ⎢−5,−5,0,5|

Let W be the subspace of R4 spanned by the vectors a = 3e1 − 4e2
and b = e2 + e3 + e4. Find the orthogonal projection of the vector
v = [2, 0, 1, 0] onto W. Then calculate the distance of the point v
from the subspace W.

U= [2,-5,-1] V=[3,2,-3] Find the orthogonal projection of u onto
v. Then write u as the sum of two orthogonal vectors, one in
span{U} and one orthogonal to U

Linear Algebra:
Find the orthogonal projection of u3=[48,-12,108] onto the plane
spanned by u1= [2,7,2] and u2=[5,35,15].
Answer Choices: [15,3,-3] [35,23,-34] [5,1,3] [-22,28,38]
[24,21,-6] [24,0,6] [34,14,18] [21,22,-11] [57,12,27]
[39,37,15]

Let W be a subspace of a f.d. inner product space V and let PW
be the orthogonal projection of V onto W. Show that the
characteristic polynomial of PW is
(t-1)^dimW t^(dimv-dimw)

let v1=[1,0,10], v2=[0,1,0,1] and let W be the
subspace of R^4 spanned by v1 and v2.
A. convert {v1,v2} into an orhonormal basis of W.
Basis =
B.find the projection of b=[-1,-2,-2,-1] onto W
C.find two linear independent vectors in R^4
perpendicular to W.
vectors =

Let W be a subspace of R^4 spanned by v1 =
[1,1,2,0] and v2 = 2,-1,0,4]. Find a basis for W^T
= {v is in R^2 : w*v = 0 for
w inside of W}

Vectors u1= [1,1,1] and u2=[8,-7,-1] are
perpendicular. Find the orthogonal projection of
u3=[65,-19,-31] onto the plane spanned by u1
and u2.

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