Question
In: Advanced Math
Use Theorem 4.2.1 to determine which of the following sets of vectors are subspaces of F(−∞,∞)....
Use Theorem 4.2.1 to determine which of the following sets of vectors are subspaces of F(−∞,∞). (Justify!)
(a) The set of all functions f ∈ F(−∞,∞) for which f(0) = 0.
(b) The set of all functions f ∈ F(−∞,∞) for which f(1) = 0.
(c) The set of all functions f ∈ F(−∞,∞) for which f(0) = 1.
(d) The set of all functions f ∈ F(−∞,∞) for which f(−x) = f(x) for all x ∈ R
Solutions
Expert Solution
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Colby Messinger answered 2 years agoRelated Solutions
Determine which of the following sets of vectors form a basis for R 3 . S...
Determine which of the following sets of vectors form a basis
for R 3 . S = {(1, 0, −1),(2, 5, 1),(0, −4, 3)}, T = {(−1, 3,
2),(3, −1, −3),(1, 5, 1)}.
Determine if each of the following sets of vectors U is a subspace of the specified...
Determine if each of the following sets of vectors U is a
subspace of the specified vector space, and if so, describe the set
geometrically:
(a) U ⊆ R2, where U = {〈x1,x2〉 : x1 = 0}
(b) U ⊆ R2, where U = {〈x1,x2〉 : x1x2 = 0}
(c) U⊆R3,whereU={〈x1,x2,x3〉:〈1,2,3〉·〈x1,x2,x3〉=0}
(d) U ⊆ R3, where U = {〈x1,x2,x3〉 : 〈1,2,2〉 · 〈x1,x2,x3〉 = 0
and
〈1, 3, 0〉 · 〈x1, x2, x3〉 = 0}
Which of the following sets are closed under addition? (i) The set of all vectors in...
Which of the following sets are closed under addition?
(i) The set of all vectors in R2 of the form (a, b) where b =
a2.
(ii) The set of all 3 × 3 matrices that have the vector [3 -1
-1]T as an eigenvector.
(iii) The set of all polynomials in P2 of the form a0 + a1 x +
a2 x2 where a0 = a2.
(A) (i) only (B) all of them (C) (ii) only (D) (i) and...
Which of the following sets are closed under addition? (i) The set of all vectors in...
Which of the following sets are closed under addition?
(i) The set of all vectors in R2 of the
form (a, b) where b = a.
(ii) The set of all 3 × 3 matrices that have the vector
[-1 3 -3]T as an
eigenvector.
(iii) The set of all polynomials in P2 of
the form a0 + a1 x
+ a2 x2 where
a0 = a22.
Which of the following sets are closed under addition? (i) The set of all vectors in...
Which of the following sets are closed under addition?
(i) The set of all vectors in R2 of the
form (a, b) where b = a.
(ii) The set of all 2 × 2 matrices that have the vector
[-2 -3]T as an eigenvector.
(iii) The set of all polynomials in P2 of
the form a0 + a1 x
+ a2 x2 where
a0 = a22.
Use normal vectors to determine the intersection, if any, for each of the following groups of...
Use normal vectors to determine the intersection, if any, for
each of the following groups of three planes. Give a geometric
interpretation in each case and the number of solutions for the
corresponding linear system of equations. If the planes intersect
in a line, determine a vector equation of the line. If the planes
intersect in a point, determine the coordinates of the point.
a x + 2y + 3z = −4
b x + 2y + 3z = −4...
For the following problems, use Octave/Matlab to determine whether the following sets
For the following problems, use Octave/Matlab to determine whether the following sets span \(\mathbb{R}^{3}\). Remember you need to pick an arbitrary element in \(\mathbb{R}^{3}\) and see if you can write it as a linear combination of the set of vectors.For each problem, do the following:1) - Write the row reduced echelon matrix found by Octave.2) - Tell me if this set spans \(\mathbb{R}^{3}\).3) - If this set spans \(\mathbb{R}^{3}\), solve for \(\alpha, \beta, \ldots\) (in other words, tell me how...
Determine all values of a for which the following set of vectors is dependent or independent....
Determine all values of a for which the following set of vectors
is dependent or independent. You can select 'always', 'never', 'a =
', or 'a ≠', then specify a value or comma-separated list of
values. ⎧ ⎪ ⎨ ⎪ ⎩⎫ ⎪ ⎬ ⎪ ⎭a001, 12−2−2, 48−8−9Dependent: When a =
0Independent: When a ≠ 0
#1 Let H= Span{v1,v2,v3,v4}. For each of the following sets of vectors determine whether H is...
#1 Let H= Span{v1,v2,v3,v4}. For each of the following sets of
vectors determine whether H is a line, plane ,or R3. Justify your
answers.
(a)v1= (1,2,−2),v2= (7,−7,−7),v3= (16,−12,−16),v4= (0,−3,−3)
(b)v1= (2,2,2),v2= (6,6,5),v3= (−16,−16,−14),v4= (28,28,24)
(c)v1= (−1,3,−3),v2= (0,0,0),v3= (−2,6,−6),v4= (−3,9,−9)
#2 Plot the linesL1: x= t[4−1] and L2: x= [−4−2] + t[4−1] using
their vector forms. If[12k]is onL2. What is the value of k?
Determine which subsets are subspaces of M 2x2 (R) and prove your answer. a. W =...
Determine which subsets are subspaces of M 2x2 (R) and prove
your answer.
a. W = {A ∈ M 2x2 (R) | a12 = -a21}
b. W = {A ∈ M 2X2 (R) | a12 = 1}
c. Fix B ∈ M 2x2 (R). Let W ={ A ∈ M 2x2 (R) | AB = BA
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