4. Let V = {ao+aj x+a2 x² | ao, a1, a2 E R} be a vector space of polynomialup to degree three, and p(x) = pPo+P1 x+p2 x², q(x)= qo+q1 x+q2 x² E Vthen show that< p(x), q(x) >= po.4o + pP1-q1 + P2-92defines an inner product on V.

To show that <p(x),q(x)>=p0q0+p1q1+p2q2 is an inner product on V and field is of ℝ, we need…

Let V = {ao+ai x+a2 x² | ao, a1, a2 E R} be a vector space of polynomial up to degree three, and p(x) = po+pi x+p2 x², q(x) = q0+q1 x+q2 x² e V then show that < p(x), q(x) >= Po•9o + P1.qi + P2-92 defines an inner product on V.

Let V = {ao+ai x+a2 x² | ao, a1, a2 E R} be a vector space of polynomial up to degree three, and p(x) = po+pi x+p2 x², q(x) = q0+q1 x+q2 x² e V then show that < p(x), q(x) >= Po•9o + P1.qi + P2-92 defines an inner product on V.

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: Let A= 00 b) Say if A is diagonalisable sur Cv H E M3x3(C) such that H-¹AH is diagonal.

Q: Let f(x) = −4, g(x) = -5x+7 and h(x) = - -2x29x+9. Consider the inner product (p,q) = p(-1)g(-1) +…

Q: (a) Consider the real linear map T : R' - R', expressed as follows: (1 2 -1 49 -1 X1 X1 + 2x2 - x3…

Q: Use Axioms only to prove that the the solution to the equation 2x + y + 3z = 0 is a subspace of R³.

A: The given equation .To prove that the solution to the equation is a subspace of .

Q: Show that the polynomials in the set do not form an orthonormal set.

A: Given, The inner product: Polynomial set:

Q: 1) Suppose Ris the set of real numbers, and we define addition (using the symbol ) as: x ® y =…

Q: The set of all polynomials of degree 6 under the standard addition and scalar multiplication…

A: Definition: A vector space is a set V on which two operations + and · are defined, called vector…

Q: The set of all polynomials of degree 4 under the standard addition and scalar multiplication…

A: (V,+, . ) is said to be vector space over the field F if (1) If (V,+) is abelian group. (2) V is…

Q: Let V = Poly2 be the vector space of polynomials of degree 2 or less and let W = Poly, be the vector…

A: Suppose we have given a linear transformation , is basis of V , is basis of W and associated…

Q: Show that λis a root of char(x) if and only if there exosts a non-zero vector v in V with L(v)=λv

A: Assume that λ is a root of charL(x) then | λIdv–L | = 0. It is known that, the system of Bx = 0 has…

Q: Suppose A is a 2x2 invertible Martix. Is the following statement true or false? For each vector b,…

Q: 1) Let v be an element of a vector space V. Prove that -(-v) = v. Your proof should work in any…

A: Here a,b are element of field.

Q: Find the dimension of the following vector spaces. (a) V = {0}: dim V = (b) V = R¹: dim V- (c) V is…

A: (.) Dimension: The number of vectors in a basis of a vector space is called dimension of..(.)…

Q: let p(x) = a0+a1x+a2x2 and q(x) = b0+b1x+b2x2 be vectors in P2 with inner product =…

Q: 19. Prove that the set of all vectors in R³that satisfy the equation x₁ = 3x2, is a subspace.

A: (.) Let set 'S' is given by , S=x1,x2,x3∈ℝ3 : x1=3x2 or S= x1,x2,x3∈ℝ3 : x1-3x2=0…

Q: One of the following vectors lies in span{ 2+x + æ2, 3+-2a2} (A) 5 + 3x + 4x2 (B) 5 + 3x + 5æ? (C) 5…

Q: Let Riz be a linear space of all polynomials p(x) = ar²+bx+c (a,b,c & R) whose degree is no more…

Q: 1 ²+1 (a) Find the inner product (f. 9) = (b) Verify the Cauchy-Schwarz Inequality. 2. Let f(x)= x…

Q: Find a basis of the subspace of R³ defined by the equation 2x1 + 3x2 + x3 = 0.

Q: 1 Defined in P,(R), p(x)=1,q(x)=x- and h(x) =x² -: -x+- 6. Investigate whether the vectors are…

Q: Consider an inner product on two P3 vectors as (f, g) = f(-1)g(-1) + f(0)g(0) + f(1)g(1) + f(2)g(2):…

A: Since you have posted multiple subpart question, we will solve the first three sub parts for you. If…

Q: A C -³/4 - 1/4 9/8 - 1/4 - 1/4 AZ = O 1/8 1/4 Find the vector 7 such that. 2 O (note: DON'T USE…

A: Give that, A-1=-34-14098-1814-14-140 and Ax→=206 We have to find the value of x→

Q: Let f(x)=-4, g(x) = -5x+7 and h(x) = -2x²-9x + 9. Consider the inner product (p,q) = p(-1)q(−1) +…

A: Step 1:Step 2: Step 3: Step 4:

Q: Show that there do not exist scalars c₁, c₂, and C3 such that c₁(1,0, 1,0) + c2 (1, 0, 2, 1) +…

Q: Give two examples of finite dimension vector spaces.

Q: Determine whether W = {ao + a1x + a2x² + a3x°|ao + a2 = az ɑ1} is a subspace of P3.

Q: the dimension of the complexification VC thought of as a real vector space

Q: Let A,X EM, (C) such that A is positive semidefinit and AX = XA Show that A¹/2X = XA¹/2.

A: Introduction: Definite matrix is significant in studying quadratic forms. Also, in Lyapunov…

Q: 7. Prove that M2x2(C) is a complex vector space under the usual addition and scalar multiplication…

Q: Is the set swer. {(1,2,-1,3), (1,-1, 2, 0), (-2, 0, 6, 6)} a basis for R¹? Justify your an-

A: BASIS:A basis for a vector space over a field is a linearly independent spanning set. In other…

Q: In RX1, let U = span ( 1 Find bases for U- and (U-)+.

Q: 1,3x-2 4. Determine whether the veltors X-I and X²-3x+2 dve lihearly independent or dependent in Pz…

Q: Suppose f is the function defined by f(x) = Ax, where a. The domain of f is b. The codomain of f is…

A: Dear student, as per our guidelines we can answer only first three subqustions. So kindly resubmit…

Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

4. Let V = {ao+aj x+a2 x² | ao, a1, a2 E R} be a vector space of polynomial
up to degree three, and p(x) = pPo+P1 x+p2 x², q(x)
= qo+q1 x+q2 x² E V
then show that
< p(x), q(x) >= po.4o + pP1-q1 + P2-92
defines an inner product on V.

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

$Vector Space$

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

1.W.4 We'll work inside the vector space of polynomials in degree < 2, which is denoted P<2. Let P1 = 1, p2 = x + 2, and p3 = (x + 2)². Leť's think about Span{p1, P2, P3}. a) What polynomial is 3p1 + 2p2 – P3? b) I claim that a = a¡P1 + a2P2 + azp3 for some coefficients a1, a2, az in R. Find a1, a2, az. Hint: az = 0. c) I claim that a? = bịPi + b2p2 + b3p3 for some coefficients b1, b2, bz in R. Find b1, b2, bz. Hint: This problem isn't quite so cut and dry. Try to find three equations, one for each coefficient in the polynomial, and solve them for b1, b2, b3.
please send handwritten solution for Q 4
1. Let V = R³. Give a definition of addition + or scalar multiplication *. on that makes (V₂+₂) unable to satisfy property Axiom 7 in the definition of vector space.
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).
Since it's an if and only if proof, don't you have to prove "if linearly dependent, then scalar multiples" and then "if scalar multiple, then linearly dependent"?
please help
Show that Null Space of Ax = 0 is a subspace.
Find the kernel and range of each of the following linear operators on P^3(the vector space of polynomials with degree less than 3):(a) L(p(x)) = xp′(x), where p′(x) is the derivative of p(x). Hint: Start with p(x) = ax2 + bx + c. (b) L(p(x)) = p(x) − p′(x).
Don't use chat gpt
One of the following vectors lies in span{ 2 + x +x², 3+x – 2x² } (A) 3 + 2x + 4x² (B) 3 + 2x + 5x² (C) 3 + 2x ++ 6x² (D) 3 + 2x + 7x² (E) 3 + 2x + 3x?
(b) (c) 0 (69) (89-19) 0 0 0 0 (6 9.89.163) 0 0 0 0 2 1 0 0 2 4. Determine whether the following vectors are lin- early independent in 2×2: 0 (@) [9] [8
8 a) 4 B) 3 NS) 2nd D) 0 TO) one