Use the Gram-Schmidt process to find an orthonormal basis for
the subspace of R4 spanned by...
Use the Gram-Schmidt process to find an orthonormal basis for
the subspace of R4 spanned by the vectors
u1 = (1, 0, 0, 0), u2 = (1, 1, 0, 0),
u3 = (0, 1, 1, 1).
Show all your work.
Let
R4
have the inner product
<u, v> =
u1v1 +
2u2v2 +
3u3v3 +
4u4v4...
Let
R4
have the inner product
<u, v> =
u1v1 +
2u2v2 +
3u3v3 +
4u4v4
(a)
Let w = (0, 6,
4, 1). Find ||w||.
(b)
Let W be the
subspace spanned by the vectors
u1 = (0, 0, 2,
1), and u2 = (3, 0, −2,
1).
Use the Gram-Schmidt process to transform the basis
{u1,
u2} into an
orthonormal basis {v1,
v2}. Enter the
components of the vector v2 into the
answer box below, separated with commas.
Use Gram-Schmidt process to transform the basis {u1, u2, u3},
where u1=(1,1,1), u2=(1,2,0), u3=(1,0,-1),:
a) for...
Use Gram-Schmidt process to transform the basis {u1, u2, u3},
where u1=(1,1,1), u2=(1,2,0), u3=(1,0,-1),:
a) for the Euclidean IPS. (IPS means inner product space)
If W is a subspace of Rn with an orthonormal basis
u1, u2, . . ....
If W is a subspace of Rn with an orthonormal basis
u1, u2, . . . , uk, if x ∈
Rn, and if
projW (x) = (x • u1)u1 + (x •
u2)u2 + · · · + (x •
uk)uk,
then x − projW (x) is orthogonal to every element of
W.
(Please show that x − projW (x) is orthogonal to each
uj for 1 ≤ j ≤ k)
u,x are vectors.
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
Use the inner product (u, v) =
2u1v1 +
u2v2 in
R2 and the Gram-Schmidt orthonormalization...
Use the inner product (u, v) =
2u1v1 +
u2v2 in
R2 and the Gram-Schmidt orthonormalization
process to transform {(?2, 1), (2, 5)} into an orthonormal basis.
(Use the vectors in the order in which they are given.)
u1 = ___________
u2 = ___________
Use the inner product <u,v>= 2u1v1 + u2v2 in R2 and the
Gram-Schmidt orthonormalization process to...
Use the inner product <u,v>= 2u1v1 + u2v2 in R2 and the
Gram-Schmidt orthonormalization process to transform {(2, ?1), (2,
6)} into an orthonormal basis. (Use the vectors in the order in
which they are given.)
u1 =
u2 =
Use the inner product u, v = 2u1v1 + u2v2 in R2 and the
Gram-Schmidt orthonormalization...
Use the inner product u, v = 2u1v1 + u2v2 in R2 and the
Gram-Schmidt orthonormalization process to
transform
{(2, ?1), (2, 6)} into an orthonormal basis. (Use the
vectors in the order in which they are given.)
u1 =
u2 =
A): compute projw j if u1=[-7,1,4] u2=[-1,1,-2],w=span{u1,u2}.
(u1 and u2 are orthogonal)
B): let u1=[1,1,1], u2=1/3...
A): compute projw j if u1=[-7,1,4] u2=[-1,1,-2],w=span{u1,u2}.
(u1 and u2 are orthogonal)
B): let u1=[1,1,1], u2=1/3 *[1,1,-2] and w=span{u1,u2}.
Construct an orthonormal basis for w.