Find the orthogonal projection of u onto the
subspace of R4 spanned by the vectors
v1,...
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
1. Find the orthogonal projection of the matrix
[[3,2][4,5]] onto the space of diagonal 2x2 matrices...
1. Find the orthogonal projection of the matrix
[[3,2][4,5]] onto the space of diagonal 2x2 matrices of the form
lambda?I.
[[4.5,0][0,4.5]] [[5.5,0][0,5.5]] [[4,0][0,4]] [[3.5,0][0,3.5]] [[5,0][0,5]] [[1.5,0][0,1.5]]
2. Find the orthogonal projection of the matrix
[[2,1][2,6]] onto the space of symmetric 2x2 matrices of trace
0.
[[-1,3][3,1]] [[1.5,1][1,-1.5]] [[0,4][4,0]] [[3,3.5][3.5,-3]] [[0,1.5][1.5,0]] [[-2,1.5][1.5,2]] [[0.5,4.5][4.5,-0.5]] [[-1,6][6,1]] [[0,3.5][3.5,0]] [[-1.5,3.5][3.5,1.5]]
3. Find the orthogonal projection of the matrix
[[1,5][1,2]] onto the space of anti-symmetric 2x2
matrices.
[[0,-1] [1,0]] [[0,2] [-2,0]] [[0,-1.5]
[1.5,0]] [[0,2.5] [-2.5,0]] [[0,0]
[0,0]] [[0,-0.5] [0.5,0]] [[0,1] [-1,0]]
[[0,1.5] [-1.5,0]] [[0,-2.5]
[2.5,0]] [[0,0.5] [-0.5,0]]
4. Let p be the orthogonal projection of
u=[40,-9,91]T onto the...
Consider the following.
u =
−6, −4, −7
, v =
3, 5, 2
(a) Find the...
Consider the following.
u =
−6, −4, −7
, v =
3, 5, 2
(a) Find the projection of u onto
v.
(b) Find the vector component of u orthogonal to
v.
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 v=[−2,10,−16,−19] onto the
subspace W spanned by [-4,0,-2,1],[-4,-2,5,1],[3,-1,-3,4]
True or False
If A is the matrix of a projection onto a line L in...
True or False
If A is the matrix of a projection onto a line L in R 2 and the
vector x in R 2 is not the zero vector, then the vector x − Ax is
perpendicular to the vector x.
If vectors u, v, x and y are vectors in R 7 such that u = 2v +
0x − 3y, then a basis for span(u, v, x, y) is {u, v, y}.
Find the orthogonal projection of v⃗ =⎢4,−11,−36,9⎤ onto the
subspace W spanned by ⎢0,0,−5,−2| , |−4,2,5,−5⎢...
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|