Question

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 = R, x + y = max( x , y ), cx=(c)(x) (usual multiplication.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
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 = R^2 , < X1 , X2 > + < Y1 , Y2 > = < X1 + X2 , Y1 +Y2> c< X1 , X2...
Exercise 9.1.11 Consider the set of all vectors in R2,(x, y) such that x + y...
Exercise 9.1.11 Consider the set of all vectors in R2,(x, y) such that x + y ≥ 0. Let the vector space operations be the usual ones. Is this a vector space? Is it a subspace of R2? Exercise 9.1.12 Consider the vectors in R2,(x, y) such that xy = 0. Is this a subspace of R2? Is it a vector space? The addition and scalar multiplication are the usual operations.
Determine if W is a subspace of R^3 under the usual addition and scalar multiplication. Either...
Determine if W is a subspace of R^3 under the usual addition and scalar multiplication. Either show algebraically that it is or show how it isn't algebraically. W= {(x1, x2, x3) ∈ R^3 x1 = x2 and x2 = 2x3 }
1. Consider the set (Z,+,x) of integers with the usual addition (+) and multiplication (x) operations....
1. Consider the set (Z,+,x) of integers with the usual addition (+) and multiplication (x) operations. Which of the following are true of this set with those operations? Select all that are true. Note that the extra "Axioms of Ring" of Definition 5.6 apply to specific types of Rings, shown in Definition 5.7. - Z is a ring - Z is a commutative ring - Z is a domain - Z is an integral domain - Z is a field...
Show that the set GLm,n(R) of all mxn matrices with the usual matrix addition and scalar...
Show that the set GLm,n(R) of all mxn matrices with the usual matrix addition and scalar multiplication is a finite dimensional vector space with dim GLm,n(R) = mn. Show that if V and W be finite dimensional vector spaces with dim V = m and dim W = n, B a basis for V and C a basis for W then hom(V,W)-----MatB--->C(-)--------> GLm,n(R) is a bijective linear transformation. Hence or otherwise, obtain dim hom(V,W). Thank you!
Consider the vector space M2x2 with the usual addition and scalar multiplication. Let it be the...
Consider the vector space M2x2 with the usual addition and scalar multiplication. Let it be the subspace of M2x2 defined as follows: H= { | a b | | c d |    with b= c} consider matrices A= | 1 2 |    B= |-2 2 |    C= | 1 8 |    | 1 3 | , | 1 -3 | ,    | 4 6 | Do they form a basis for H? justify the answer
Let S={(0,1),(1,1),(3,-2)} ⊂ R², where R² is a real vector space with the usual vector addition...
Let S={(0,1),(1,1),(3,-2)} ⊂ R², where R² is a real vector space with the usual vector addition and scalar multiplication. (i) Show that S is a spanning set for R²​​​​​​​ (ii)Determine whether or not S is a linearly independent set
Consider the set of all ordered pairs of real numbers with standard vector addition but with...
Consider the set of all ordered pairs of real numbers with standard vector addition but with scalar multiplication defined by  k(x,y)=(k^2x,k^2y). I know this violates (alpha + beta)x = alphax + betax, but I'm not for sure how to figure that out? How would I figure out which axioms it violates?
Let V=R2 with the standard scalar multiplication and nonstandard addition given as follows: (x1, y1)⊕(x2, y2)...
Let V=R2 with the standard scalar multiplication and nonstandard addition given as follows: (x1, y1)⊕(x2, y2) := (x1x2, y1+y2). Show that (V,⊕, .) is not a vector space.
3. Closure Properties (a) Using that vector spaces are closed under scalar multiplication, explain why if...
3. Closure Properties (a) Using that vector spaces are closed under scalar multiplication, explain why if any nonzero vector from R2 or R3 is in a vector space V, then an entire line’s worth of vectors are in V. (b) Why isn’t closure under vector addition enough to make the same statement? 4. Subspaces and Spans: The span of a set of vectors from Rn is always a subspace of Rn. This is relevant to the problems below because the...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT