Determine if the vector v is a linear combination of the vectors
u1, u2, u3. If...
Determine if the vector v is a linear combination of the vectors
u1, u2, u3. If yes, indicate at least one possible value for the
weights. If not, explain why.
v =
2
4
2
, u1 =
1
1
0
, u2 =
0
1
-1
, u3 =
1
2
-1
Let B1 = { u1, u2, u3 }, where u1 = (2,?1, 1), u2 = (1,?2,...
Let B1 = { u1, u2, u3 }, where u1 = (2,?1, 1), u2 = (1,?2, 1),
and u3 = (1,?1, 0). B1 is a basis for R^3 .
A. Find the transition matrix Q ^?1 from the standard basis of R
^3 to B1 .
B. Write U as a linear combination of the basis B1 .
Consider the vector: u1=(1,1,1), u2= (2,-1,1), u3=(3,0,2),
u4=(6,0,4)
a)Plot the dimension and a basis for W=...
Consider the vector: u1=(1,1,1), u2= (2,-1,1), u3=(3,0,2),
u4=(6,0,4)
a)Plot the dimension and a basis for W= span {u1,u2,u3,u4}
b)Does the vector v= (3,3,1) belong to W? justify the
answer.
c) Is it true that W= span{ u3,u4} Justify answer.
5. Let U1, U2, U3 be subspaces
of a vector space V.
Prove that U1, U2,...
5. Let U1, U2, U3 be subspaces
of a vector space V.
Prove that U1, U2, U3 are
direct-summable if and only if
(i) the intersection of U1 and U2 is 0.\,
and
(ii) the intersection of U1+U2 and
U3 is 0.
A detailed explanation would be greatly appreciated :)
Linear Algebra
Write x as the sum of two vectors, one is Span {u1,
u2, u3}...
Linear Algebra
Write x as the sum of two vectors, one is Span {u1,
u2, u3} and one in Span {u4}. Assume that
{u1,...,u4} is an orthogonal basis for
R4
u1 = [0, 1, -6, -1] , u2 = [5, 7, 1, 1],
u3 = [1, 0, 1, -6], u4 = [7, -5, -1, 1], x =
[14, -9, 4, 0]
x =
(Type an integer or simplified fraction for each matrix
element.)
Consider the vector u1=(2,0,2), u2=(4,1,-1), u3=( 0,1,-5),
u4=(3,0,2)
a) Find the dimension and a basis for...
Consider the vector u1=(2,0,2), u2=(4,1,-1), u3=( 0,1,-5),
u4=(3,0,2)
a) Find the dimension and a basis for U= span{ u1,u2,u3,u4}
b) Does the vector u=(2,-1,4) belong to U. Justify!
c) Is it true that U = span{ u1,u2,u3} justify the answer!
If v1 and v2 are linearly independent vectors in vector space V,
and u1, u2, and...
If v1 and v2 are linearly independent vectors in vector space V,
and u1, u2, and u3 are each a linear combination of them, prove
that {u1, u2, u3} is linearly dependent.
Do NOT use the theorem which states, " If S = { v 1 , v 2 , . . . ,
v n } is a basis for a vector space V, then every set
containing
more than n vectors in V is linearly dependent."
Prove without...
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)
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.
Let W be the subspace of R4
spanned by the vectors
u1 = (−1, 0, 1,...
Let W be the subspace of R4
spanned by the vectors
u1 = (−1, 0, 1, 0),
u2 = (0, 1, 1, 0), and
u3 = (0, 0, 1, 1).
Use the Gram-Schmidt process to transform the basis
{u1, u2,
u3} into an orthonormal basis.