Question
In: Advanced Math
Which of the following sets are closed under addition? (i) The set of all vectors in...
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Solutions
Colby Messinger answered 10 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.
Let ?V be the set of vectors in ?2R2 with the following definition of addition and...
Let ?V be the set of vectors in ?2R2 with the following
definition of addition and scalar multiplication:
Addition: [?1?2]⊕[?1?2]=[0?2+?2][x1x2]⊕[y1y2]=[0x2+y2]
Scalar Multiplication: ?⊙[?1?2]=[0??2]α⊙[x1x2]=[0αx2]
Determine which of the Vector Space Axioms are satisfied.
A1. ?⊕?=?⊕?x⊕y=y⊕x for any ?x and ?y in ?V
? YES NO
A2. (?⊕?)⊕?=?⊕(?⊕?)(x⊕y)⊕z=x⊕(y⊕z) for any ?,?x,y and ?z in
?V
? YES NO
A3. There exists an element 00 in ?V such that ?⊕0=?x⊕0=x for
each ?∈?x∈V
? YES NO
A4. For each ?∈?x∈V, there exists an...
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) a. Which of the following sets are the empty set? i. { x | x...
1)
a. Which of the following sets are the empty
set?
i. { x | x is a real number and x2 – 1 = 0 }
ii. { x | x is a real number and x2 + 1 = 0 }
iii. { x | x is a real number and x2 = -9 }
iv. { x | x is a real number and x = 2x + 1 }
b. Let A = {1, 2, 3,...
Determine whether the set with the definition of addition of vectors and scalar multiplication is a...
Determine whether the set with the definition of addition of
vectors and scalar multiplication is a vector space. If it is,
demonstrate algebraically that it satisfies the 8 vector axioms. If
it's not, identify and show algebraically every axioms which is
violated. Assume the usual addition and scalar multiplication if
it's not identified. V = R^2 , < X1 , X2 > + < Y1 , Y2
> = < X1 + Y1 , 0> c< X1 , X2 >...
Determine whether the set with the definition of addition of vectors and scalar multiplication is a...
Determine whether the set with the definition of addition of
vectors and scalar multiplication is a vector space. If it is,
demonstrate algebraically that it satisfies the 8 vector axioms. If
it's not, identify and show algebraically every axioms which is
violated. Assume the usual addition and scalar multiplication if
it's not defined. V = { (x1, x2, x3) ∈ R^3 | x1 > or equal to 0,
x2 > or equal to 0, x3 > or equal to 0}
Determine whether the set with the definition of addition of vectors and scalar multiplication is a...
Determine whether the set with the definition of addition of
vectors and scalar multiplication is a vector space. If it is,
demonstrate algebraically that it satisfies the 8 vector axioms. If
it's not, identify and show algebraically every axioms which is
violated. Assume the usual addition and scalar multiplication if
it's not defined. V = { f : R --> R | f(1) = 0 }
Determine whether the set with the definition of addition of vectors and scalar multiplication is a...
Determine whether the set with the definition of addition of
vectors and scalar multiplication is a vector space. If it is,
demonstrate algebraically that it satisfies the 8 vector axioms. If
it's not, identify and show algebraically every axioms which is
violated. Assume the usual addition and scalar multiplication if
it's not defined. V = {all polynomials with real coefficients with
degree > or equal to 3 and the zero polynomial}
Which of the following sets are rings with respect to the usual operations of addition and...
Which of the following sets are rings with respect to the usual
operations of addition and multiplication? If the set is a ring, is
it also a field? can you explain in detail, I really do not
understand how to prove.
Q(√2,√3)={a+b√2+c√3+d√6:a,b,c,d∈Q}
R={a+b3√3:a,b∈Q}
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