ZuoTi.Pro
Question

b) Show that V -(x, y, 2)lr-y2z 2 is not a vector space under the standard operations of vector addition and scalar multiplication.

math   algebra   
0 0
Add a comment Improve this question Transcribed image text
Next > < Previous
Sort answers by oldest

Homework Answers

Answer #1

The set V (w t sandad addihon and scalan multiplicahon ) is not a vecdon space (4) Check u,VGV → u+VGV closure undo addton Let uveV, ehat s u,and v aie solutons to the such that ul-u2+2y3=2 and v,-½t2k-2 xu,vev utve V doesnt hold he,fo nstan e u (0,0,1) and v-C1,-1,๐) (both one mv sna both me solrhons to 2-y+az=2) Then uw C, but 2) 4 and thfore u+ s not a soluhon to (0)-(0) + 2A)ニ4+2) . Therefore not closed unde Sc mulhiplication ce (S

0 0
Add a comment
Know the answer?
Add Answer to:
b) Show that V -(x, y, 2)lr-y2z 2 is not a vector space under the standard...
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. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions

  • CAN ANYONE HELP WITH LINEAR ALGEBRA 1. Verify if the following is a vector space. If...

    CAN ANYONE HELP WITH LINEAR ALGEBRA 1. Verify if the following is a vector space. If it is not, then show which of the 10 vector space axioms fail. The set of all vectors in with x > 0, with the standard vector addition and scalar multiplication. 2. Verify if the following is a vector space. If it is not, then show which of the 10 vector space axioms fail. The set of all vectors in R" of the form...

  • 1/2 b dr Problem 1: Suppose that [a, b] exists R, and let V be the space of all functions for which and is finite. For...

    1/2 b dr Problem 1: Suppose that [a, b] exists R, and let V be the space of all functions for which and is finite. For two functions f and g in V and a scalar A e R, define addition and scalar multiplication the usual way: (Af)(x) f(x) f(x)g(r) and (fg)(x) Verify that the set V equipped with the above operations is a vector space. This space is called L2[a, b 1/2 b dr Problem 1: Suppose that [a,...

  • 1. Why the following sets are not vector space? with the regular vector addition and scalar...

    1. Why the following sets are not vector space? with the regular vector addition and scalar multiplication. a) V = {E: * > 0, y 20 with the regula b) V = {l*: *y 2 o} with the regular vector addition and scalar multiplication. c) V = {]: x2+y's 1} with the regular vector addition and scalar multiplication. 2. The set B = {1,1+t, t + t2 is a basis for P, the set of all polynomials with degree less...

  • I. Consider the set of all 2 × 2 diagonal matrices: D2 under ordinary matrix addition and scalar multiplication. a....

    I. Consider the set of all 2 × 2 diagonal matrices: D2 under ordinary matrix addition and scalar multiplication. a. Prove that D2 is a vector space under these two operations b. Consider the set of all n × n diagonal matrices: di 00 0 d20 0 0d under ordinary matrix addition and scalar multiplication. Generalize your proof and nota in (a) to show that D is a vector space under these two operations for anyn I. Consider the set...

  • For each of the following sets, indicate whether it is a vector space. If so, point...

    For each of the following sets, indicate whether it is a vector space. If so, point out a basis of it; otherwise, point out which vector-space property is violated. 1.The set V of vectors [2x, x2] with x R2. Addition and scalar multiplication are defined in the same way as on vectors. 2.The set V of vectors [x, y, z] R3 satisfying x + y + z = 3 and x − y + 2z = 6. Addition and scalar...

  • V01 (version 953): Let V be the set of all pairs (x,y) of real numbers together...

    V01 (version 953): Let V be the set of all pairs (x,y) of real numbers together with the following operations: (x1, yı) © (C2, y2) = (x1 + 22,41 + y2) cº (x, y) = (Acc, 4cg). (a) Show that scalar multiplication distributes over scalar addition, that is: (c+d) 9 (z, 3) = c+ (x, y) #de (x, y). (b) Explain why V nonetheless is not a vector space.

  • Show that the following are not vector spaces: (a) The set of all vectors [x, y]  in R...

    Show that the following are not vector spaces: (a) The set of all vectors [x, y]  in R^2 with x ≥ y, with the usual vector addition and scalar multiplication. ------------------------------------------------[a b] (b) The set of all 2×2 matrices of the form [c d] in where ad = 0, with the usual matrix addition and scalar multiplication. I need help with this question. Could you please show your work and the solution.

  • Math 407 Homework 4 Name: 1. Why the following sets are not vector space? with the...

    Math 407 Homework 4 Name: 1. Why the following sets are not vector space? with the regular vector addition and scalar multiplication. b) v = {(7: «y 20} with the regular vector addition and scalar multiplication. with the regular vector addition and scalar multiplication. 2. The set B = {1,1+t, t+t?} is a basis for P, the set of all polynomials with degree less than or equal to 2. Find the coordinate vector of p(t)-5+21+342 3. Let H =Span{ői, üz.us)...

  • Need to use all axioms to prove this is a vector space. e(a+b)z and scalar multiplication...

    Need to use all axioms to prove this is a vector space. e(a+b)z and scalar multiplication as feax a E R} define addition as ea* + ebx ekax where k e R. Is V a vector space under these definitions? If so, what is the 0 element = eaeba- 8. Let V = k ea of V? e(a+b)z and scalar multiplication as feax a E R} define addition as ea* + ebx ekax where k e R. Is V a...

  • Question 1: Vector Spaces and Subspaces (a) Show that (C(0, 1]), R, +,), the set of...

    Question 1: Vector Spaces and Subspaces (a) Show that (C(0, 1]), R, +,), the set of continuous functions from [0, 1 to R equipped with the usual function addition and scalar multiplication, is a vector space. (b) Let (V, K, +,-) be a vector space. Show that a non-empty subset W C V which is closed under and - necessarily contains the zero vector. (c) Is the set {(x,y)T: z,y E R, y a subspace of R2? Justify.

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT