Let V=R? and let (R²)* be the dual space for R?.Find the basis {o1, 02} that is dual to the following basis of R?: {vi=(2, -2.), v2=(0, 2 )}.Find the basis {V1, V2} of R? that is dual to the basis {01, 02} of (R?)* defined byd1(x, y)=2 x+2y;02(x, y)=2x;

Answered: Image /qna-images/answer/fbe5bd36-9d68-4cb7-84e9-22f0c771a1f3.jpg

Let V=R? and let (R?)* be the dual space for R?. Find the basis {oı, 02} that is dual to the following basis of R?: {v=(2,-2.), v2=(0, 2 )}. Find the basis {V1, V2} of R² that is dual to the basis {01, 02} of (R²)* defined by d1(x, y)=2 x+2y: (x, y)=2x;

Let V=R? and let (R?)* be the dual space for R?. Find the basis {oı, 02} that is dual to the following basis of R?: {v=(2,-2.), v2=(0, 2 )}. Find the basis {V1, V2} of R² that is dual to the basis {01, 02} of (R²)* defined by d1(x, y)=2 x+2y: (x, y)=2x;

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.3: Matrices For Linear Transformations

Problem 52E: Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.

See similar textbooks

Related questions

Q: Find a basis for the plane 4 + 3y + 5z = 0 in R. %3D

Q: Let B = {v1,..., Vn} be an orthonormal basis for R". (a) Prove Parseval's Identity, that is, for any…

A: According to the given information,

Q: the coordinates of (2, 3, 4, – 1) with B = {(1, 1, 1, 2), (1, –1, 0, 0), (0, 0, 1, 1), (0, 1, 0, Q}}…

Q: Find the missing coordinates such that the three vectors form an orthonormal basis for R' : 0.6 0.8…

A: Given0.60.8a , bc1 , d0.6eWe need to find a,b,c,d,e , such that the three vectors form an…

Q: The Gram-Schmidt process transforms the basis u=(-1, 3), u2=(7, – 1) of R²into the orthogonal basis…

A: We have given the basis u1=-1,3 and u2=7,-1. The Gram-Schmidt process to convert basis into the…

Q: Show that ?? = {(1,2,3), (−1, −1,1), (5, −4,1)} is an orthogonal basis of ℝ3, and use the Fourier…

A: Definition: A subset of a vector space V is linearly independent, if Theorem: If is a orthogonal…

Q: Let {x, y} be a basis for a vector space V. Show that both {x + y, ax} and {ax, by} are bases for V,…

Q: Consider the set P= {1+2x,-1-x+x*,x+x,1+2x+x}. i. Determine if the set P spans the vector space P, ,…

Q: Let V=R with Euclidean Inner Product, and let W = span{v1, V2, V3 where Vi = (1,0,-4, 0, 2), v2 =…

Q: The Gram-Schmidt process transforms the basis u=(1, 2), U2 =(6, 2) of R into the orthogonal basis…

Q: Using the Gram-Schmidt procedure, give an orthogonal basis {x1, x2, x3} for R°, starting with the…

Q: (d) Show that the polynomials P₁ = 3 + 2x + x², P₂ = 2x+3x², p3= −2+x=2x² form a basis of the vector…

A: Using 1+2x-x^2=ap1+bp2+cp3 find a b c

Q: b) Let Pn be a vector space consisting of polynomials of at most degree n. The standard basis for P,…

A: value of k is 0 see calculation below

Q: Let B = {v1,...,Vn} be an orthonormal basis for R". (a) Prove Parseval's Identity, that is, for any…

A: According to the given information,

Q: 1. Let {V1,... , Vn} be an orthogonal basis of R". For any vectors x, y in R" show that (x . V;) (y…

Q: V is the linear span of the polynomials a =x' + 2x – 2x + 1, ß=x' + 3x² - x+4, y = 2x +x - 7x – 7…

Q: The Gram-Schmidt process transforms the basis u,=(1, –3), u2=(-7, 1) of R- into the orthogonal basis…

Q: (a) Find an orthonormal basis of the vector space P₂ of polynomials of degree at most 2 with respect…

Q: Recall that B = {1+2x,3 – x}. Let the vector space P¡ have the inner product (p, q) = 2aobo + 3a¡b¡…

A: Given B=1+2x,3-x is basis of the vector space P1. The inner product , defined on P1 as follows:…

Q: ()--) U1 Let V = C2, and for u = V1 V = E V, define %3| U2 V2 (u, v) = u101 + iujū2 – iuzī1 + 2uzī2.…

A: Step:-1 Note:- Let V be a vector space and a, b, c∈V then an inner product , on V is a operation…

Q: The Gram-Schmidt process transforms the basis u= (1, -2) , u2= (2, 6) of R into the orthogonal basis…

Q: Let V be the vector space of polynomials of degree < 2 with real coefficients, endowed with the…

Q: Using the Gram-Schmidt procedure, give an orthogonal basis {x1, x2, x3} for R°, starting with the…

A: Given v1=12-2,v2=00-1,v3=010. Find the orthogonal basis x1,x2,x3 using the gram schmidth.

Q: Let R4 have the Euclidean inner product. Use the Gram- Schmidt process to transform the basis…

Q: The Gram-Schimidt process transforms the basis u=(1, 3), u2-(1, -7) of R intothe orthogonal basis…

A: Given u1=⟨1,3⟩,u2=⟨1,−7⟩

Q: Find an prthonormal basis of the plane x1+ 2x2- x3 0.. W

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find an orthonormal basis of the plane x1 + 8x2 – x3 = 0.

A: That's easy. Have a great day!!!

Q: F: R3→R3 whose kernel is spanned by u1=( 2, 2, 1) and u2=(1, 0, 2) Find a basis and the dimension…

Q: The following vectors u,, u,, and u, form an orthonormal basis for R³. (금이) u, = (0, –1, 0), u2 = 0,…

A: We find the required linear combination

Q: In the vector space P,, of polynomials of degree at most two, the coordinates of the vector P(x)…

Q: Expand x = (a, b, c, d) with respect to the orthogonal basis of: 2 -1 1 Vị = V2 -2 3 Express your…

A: Note: Observe that the given orthogonal basis spans only two dimension subspace of ℝ4, therefore the…

Q: 4. Let {V1, ... , Vn} be an orthogonal basis of R". For any vectors x, y in R" show that Σ (х - V,)…

Q: 4 U2 = be a basis for R². Use the Gram-Schmidt process to find an orthogonal Let basis under the…

A: If u1,u2, …un is a basis of ℝ2, then by Gram-Schmidt orthogonalization process v1,v2, …vn is an…

Q: Find x with respect to the standard basis corresponding to the coordinate vector [x]g and basis B. 2…

Q: The Gram-Schmidt process transforms the basis u3(1,-3), u,=(-7, 1) of R into the orthogonal basis…

Q: The Hermite polynomials form an orthogonal (not orthonormal) basis with this inner product: (Hm[Hn)…

A: Given: fx=x3…

Q: The Gram-Schmidt process transformsthe basis u1=(-3,1), u2=(7, 1) of R´ into the orthogonal basis…

A: Orthogonal set problem....

Q: The Gram-Schmidt process transforms the basis u1=(-1, 2), uz=(6, –2) of R into the orthogonal basis…

Q: Let V be the vector space of polynomials of degree < 2 with real coefficients, endowed with the…

Q: (a) Show that the list {p o(x), p 1(x), p 2(x), ...,p n(x),...,} where po(x) = 1, p1(x) = 1+x, P;(x)…

Q: The Gram-Schmidt process transforms the basis u=(1, 2), u2 =(6, 2) of R2 into the orthogonal basis…

Q: 3 Let U2 = -3 Uz be a basis for IR³. Use the Gram-Schmidt process to find an orthogonal basis under…

A: Using Gram-Schmidt, to find orthogonal basis and compare V1, V2, V3.

Q: Find an orthonormal basis of the plane x1+ 5x2 – x3 = 0. }

A: Introduction: A set of vectors that is orthogonal to each other and spans a plane is the set of…

Q: Given basis B = {(1, -1), (2, 3)} and basis C = {(1, 0), (0, 1)}, and linear map T = (x + 2y ; 2x -…

Q: Use the Gram-Schmidt process to transform the given basis {w1, W2, W3} into an orthogonal basis…

Q: The Gram-Schmidt process transforms the basis u=(1, 2), u2 =(6, 2) of R² into the orthogonal basis…

Q: The Gram-Schmidt process transforms the basis u=(-1,3), u2-(7,-1) of R into the orthogonal basis…

A: Let u1, u2, u3,...un is a basis for an inner product space V. Using Gram-Schmidt orthogonalization…

Q: The Gran-Schmidt process t ransforns the basis u,-(-3,1), uz-(7, 1) of R into the orthogonal basis…

Q: Explain how fixing a basis v1, , Vn of V associates to a quadratic form a corresponding function in…

A: To explain how a basis v1,v2,...,vn associates to a quadratic form of a corresponding function in n…

Q: Let {u1 (x) = 6, uz (2) = 12x, uz (x) = --12x} be e basis for a subepace of PUse the Gram- Schmidt…

A: Let {u1(x)=6, u2(x)=-12x, u3(x)=-12x2} be a basis for a subspace of P2.f,g=∫01f(x)g(x)dx on C[0,1]

Question

Let V=R? and let (R²)* be the dual space for R?.
Find the basis {o1, 02} that is dual to the following basis of R?: {vi=(2, -2.), v2=(0, 2 )}.
Find the basis {V1, V2} of R? that is dual to the basis {01, 02} of (R?)* defined by
d1(x, y)=2 x+2y;
02(x, y)=2x;

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

Step 2

Step 3

Step 4

Step 5

Step by step

Solved in 5 steps with 7 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Inner Product Spaces$

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.