1) The space (R²,O,O) is not a vector space where:(x, y) O (z, w) = (x +z + 1, y + w +1)a © (x,y) = (ax, ay)%3DWrite down the axioms that fail to hold.1

A vector space is defined over field F that consists of a set on which two operations (addition and…

Answered: 1) The space (R²,O,O) is not a vector…

1) The space (R²,O,O) is not a vector space where: (x, y) O (z, w) = (x + z + 1, y + w + 1) a O (x, y) = (ax, ay) %3D Write down the axioms that fail to hold.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Find one voctor in R' that spans the intersoction of U and W where U is the xy-plane-that is, U =…

Q: Consider the inner product space (P2, (, )) with (p, q) = p(to)q(to) + p(t1)q(t1) + p(t2)q(t,),…

Q: 6. (a) Let u, v, w be three linearly independent vectors in Euclidean Space R^7. Determine a value…

A: we have to find the value of for the linearly dependent and linearly independent

Q: 7 Given the inner product space (R³(R),+,·,· ), where xoy = 3x₁y₁ + 2(x₂Y₁ + X₁Y₂) + 3x₂Y/₂ + 2x3V3,…

Q: If x, y and z are vectors in an inner product space such that (x, y) = (x, z), then y = 2.

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Set V = {(x, y) | x ER, YER}. Define addition of vectors by the rule (x, y) + (x, y) = (y + y',x+x')…

Q: 6. Let V be a vector space over F and let u, v, we V, a, Be F. Which of the following is not a…

A: In this question, we will discuss about the properties of vector space.

Q: Let V = Colz be the vector space of 3-dimensional column vectors and let W = Poly, be the vector…

Q: Show that (x, y) = 5x1y1 – 9x2y2 for vectors x = (x1, x2) and y = (y1, y2) in R2 defines an inner…

A: This question is about application of linear algebra

Q: H.W: Let V = R2, defined the addition by: (u1 +u2) + (V1 +v2)= ( U1 +V1 , U2 +V2 + 1) With standard…

Q: (2) Let M₂×2 be the vector space of all 2X2 matrices, and defined T:M 2x2 (A)=A+AT. where A= a [cd]…

A: Given the vector space of all matrices, and defined , such that where .The aim is to describe the…

Q: 6) Consider the following vector spaces with corresponding basis: V₁ =R³ Bv₁ = {e₁,e2, е3} Bw₁ = {1,…

Q: W4 Pick any vector space V that you want, as long as dim(V) ≥ 6. Then, pick 4 vectors in the space,…

Q: A student learning about linear independence makes the following inaccurate statement: "A subset S…

A: We have to solve given problem:

Q: if u and y are vectors in a vector space and (u, v) is an inner product then which one of the…

A: If u¯ and v¯ are vectors in a vector space and ⟨u¯,v¯⟩ is an inner product.

Q: 6. Let V be the vector space of all diagonal 5 x 5 matrices, then dim(V)=--

A: Given that the vector space contains all diagonal 5×5 matrices and we need to find its dimension.

Q: Find the next vector spacing and wrap A = 1(x + y?) +jv² + zx) + k(z? + xy)

Q: Find the point on the line T = (-2, 2, 3) + t(4, 1, 1) that presents the shortest distance to the…

Q: Let U = ((1, 1, 0, 1), (0, 1, 2, 3), (2, 3, 2,−1)) and W = ((1, 3, 4, 4), (1, 1, 0, 2)) be sub-…

A: The given U=1, 1, 0, 1, 0, 1, 2, 3, 2, 3, 2, -1 and W=1, 3, 4, 4, 1, 1, 0, 2 be a subspaces of ℝ4.…

Q: Q1. If O (0,0,0) in (x,y,z) 3-D space and r(2,5,1) draw the vector in 3D and find its direction.

A: Plot point in 3D

Q: C along with the following operations defined: (a1, a2) + (b1, b2) =(a1 +b1 + 1, az + b2 +1) C •…

Q: HIf vectors x, y, z, u in the real vector space p (the polynomials) are defined by x(t)=1, y (t)=t,…

Q: Find ProjS(u) where S is the space spanned by v1= (1/3)(2,1,2) and v2= (1/3)(-2,2,1). Find the…

Q: Let V = R' and define vector addition as (x, y, z)+(x', y', z')= (x+x',y+y',z+z') (standard…

Q: 3) Let (v,, vy, v) be a set of vectors from a vector space R', then: a) The vectors are linearly…

Q: Let V = {(x,y) where y= 3x+1 x ER} with scalar multiplication defined by k(x,y)=(kx,y) is a vector…

Q: Q2) Show that (R², R , +,.) is a vector space or not? Under additional and scalar multiplication on…

A: Vector Space: A set V is called vector space over the scalar field F if two operations + and · are…

Q: Verify all vector space axioms under the given operations (x,y,z)+(x',y'z') = (x+x'+1,y+y'+2,z+z'+3)…

A: The objective of the question is to verify if the given operations satisfy all the axioms of a…

Q: Show that in 3D space, (a) k EijkEpqk = δip&jq – διαδjp

A: Note: Since you have posted multiple questions, we will solve first question for you. Kindly repost…

Q: The inner product, (alb), of any two vectors a and b in a vector space must satisfy the conditions…

Q: Let R" be a real vector space, and u = (u1, u2, Un), v = (v1, V2, ..., Vn) E .... R", then show that…

A: For a real vector space, the inner product . , . satisfies the following properties a) u+w , v =…

Q: 10) (6 points) Using the inner product (v, w) = 3v¡W1+5v2W2 with the vector space R?. a) Find a…

Q: d). Let K = {(x;y) | x,y e R} with operations (x1;y1) (X2;y2) = (x, + x2 + 1; y, +y2 - 2) %3! (ax, +…

A: Given: K=x;y | x, y∈ℝ with operations x1, y1⊕x2, y2=x1+x2+1; y1+y2-2 and a⊗x1;y1=ax1+a-1; ay1-2a+2.…

Q: V = M ₂x2 (IR) let M = { A€ V A = A} N = {A = V A = - A^²} Subset of the vector space V The answer V…

A: To prove V=M⊕N we need to prove (i) V=M+N and (ii) M∩N=0

Question

1) The space (R²,O,O) is not a vector space where:
(x, y) O (z, w) = (x +z + 1, y + w +1)
a © (x,y) = (ax, ay)
%3D
Write down the axioms that fail to hold.
1

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Projection$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

4) Let V be the vector space of polynomials of degree <2 and let p(x) = ax² + bx + c. Find the adjoint operator (T*@)(p) for T:V → V and o:V → R given by d) Tp(x) = x²p(x) + x³p'(x), @(p) = p"(1).
5. Find the orthogonal projection of the vector b = vectors V₁ = -1- and v2 = onto the subpace E spanned by the (Note that v₁ V₂).
Plz do both subparts
8.) find a vector of norm 2 that is orthogonal to the three vectors, u=(2,1,0), v=(-1,- 1,0) and w=(4,0,0) 9.) find scalars a, b and c such that a(2,0,1) +b (1,3,2)+c(1,0,1)=(7,3,4)
Let V be the vector space of functions spanned by B = {bị 2 sin r + 6 cos a, b2 = 3 sin a + 7 cos a} where a + %3D C = {ci = sin a, c2 = of coordinates matrix P ne Z is also a basis for V. Find the change 2 = cos a} where a + C+B Ex: 5 P = C-B The coordinates of a function f(x) relative to the basis B are [f(x)]B Find the coordinates of f(æ) relative to Cand find f(æ). Ex: 5 [f(x)]c = f(x) = Ex: 5 sin z + cos a
11. Let (V, (, )) be a complex inner product space. For vectors v, w, set (v, w) R = ¹/[(v, w)+(w, v)]. Consider V to be a real vector space. Is (V, (, )R) an inner product space? Support your answer with a proof.
b) Verify that the following is an inner product on R² where u = (x1, x2) , v = (yı, Y2) f(u, v) = x,Y1 – 2x1Y2 – 2x,y1 + 5x2Y2 Also explain whether inner product of two vectors is same as the usual product of two vectors. i) ii) If u = (2,3) , v = (1, 5), then find inner product of u, v by using above product . Normalize the vectors u, v.
Compute the curl of each of the following vectors: V = (yz, xz, xy) F = (x, y, z) = = ( Note: Y 2 (x² + y² +2²)³/²¹ (x² + y² + x2)³/²¹ (x² + y² + x2)³/2 • If the answer is a scalar, you can just type it in the box (using the Calcpad if you like, or using / for fractions, ^ for exponents, etc.) For multiplication, you can either leave a space, or use *. So x*x=xx = x². Note that this is not the same as xx without a space; that will get read as an entirely different variable! • If you need to enter a vector, enter an ordered list of components, so for A you can enter either A = (A₂, Ay, A₂) = {Ax, Ay, Az} . Note that the system isn't great with multiplying through by overall factors, so it's better not to write e.g. • If you need to enter O, enter it in three components, as (0, 0, 0) or {0,0,0}. V x V = ▼ xr= vx= (2A, 2A, 2A₂).
3. (12) Let V = R². Define vector addition and scalar multiplication as follows: (u1, uz)O(v1, v2) = (u1V1, U2V2) and c(u1,u2) = (u,C, u2^), c > 0 (a) Does V have an additive identity? If so, what would it be? (b) Does the distributive axiom c(uOv) = cu@cv hold? (Show why or why not). 4