Question
In: Advanced Math
Consider the following sets. (i) All vectors (a, b) in R2 such that ab ≠ 0....
Consider the following sets.
Determine whether each of the above sets is closed under addition or NOT closed under addition . |
Solutions
Colby Messinger answered 3 months agoRelated Solutions
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.
Consider the following vectors: →a = 5 −1 3 3 →b = 5 0 1 0...
Consider the following vectors:
→a =
5
−1
3
3
→b =
5
0
1
0
→c =
−10
3
−3
−7
For each of the following vectors, determine whether it is in
span{→a, →b, →c}. If so, express it as a linear combination using
a, b, and c as the names of the vectors above.
→v1 =
5
−3
2
7
< Select an answer >
→v2 =
2
7
6
−7
< Select an answer >
→v3 =...
Consider the following relations: R1 = {(a, b) ∈ R2 ∣ a > b}, the greater...
Consider the following relations:
R1 = {(a, b) ∈
R2 ∣ a > b}, the
greater than relation
R2 = {(a, b) ∈
R2 ∣ a ≥ b}, the
greater than or equal to relation
R3 = {(a, b) ∈
R2 ∣ a < b}, the
less than relation
R4 = {(a, b) ∈
R2 ∣ a ≤ b}, the less
than or equal to relation
R5 = {(a, b) ∈
R2 ∣ a = b}, the
equal to relation...
Find a pair of vectors, a → and b → that satisfy all of the following...
Find a pair of vectors, a → and b → that satisfy all of the
following conditions:
a → + b → = 〈 9 , 5 , 5 〉
a → is parallel to 〈 5 , 1 , 2 〉
b → is orthogonal (perpendicular) to {5,1,2}
(3) Consider the linear map ? : R2 → R2 which sends (1, 0) ↦→ (−3,...
(3) Consider the linear map ? : R2 → R2 which sends (1, 0) ↦→
(−3, 5) and (0, 1) ↦→ (4, −1).
(a) What is the matrix of the transformation? What is the change
of coordinates matrix? Do they agree? How come?
(b) Where does this transformation send the area between the
vector (4, 2) and the x-axis? Explain algebraically and draw a
picture.
(c) What is the image of the lower half plane under ?? Explain
algebraically and...
Consider the following fragment of C code: for (i=0; i<100; i++) { A[i]=B[i]+C; } Assume that...
Consider the following fragment of C code:
for (i=0; i<100; i++) {
A[i]=B[i]+C;
}
Assume that A and B are arrays of 64-bit integers, and C and i
are 64-bit integers.
Assume that all data values and their addresses are kept in
memory (at
addresses 1000, 3000, 5000, and 7000 for A, B, C, and i,
respectively) except when
they are operated on. Assume that values in registers are lost
between iterations of
the loop. Assume all addresses and words...
Give examples of sets of three vectors that are: a) Collinear b) Coplanar c) Not coplanar
Give examples of sets of three vectors that are:
a) Collinear
b) Coplanar
c) Not coplanar
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}
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