Answered: Let ̄f = c1φ1 + c2φ2 + ... + cnφn be…

Let ̄f = c1φ1 + c2φ2 + ... + cnφn be the projection of f on the orthogonal set (φ1,φ2,...φn). Show that f − ̄f is orthogonal to each of the functions (φ1,φ2,...φn).

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.5: Permutations And Inverses

Problem 10E: 10. Let and be mappings from to. Prove that if is invertible, then is onto and is...

See similar textbooks

Related questions

Q: You are given two random variables X and Y. E(X) = 0.5, Var(X) = 2 E(Y) = 7, Var(Y) = 3.5 cov (X, Y)…

A: What is Variance: Variance is a spread measure for a random variable distribution that quantifies…

Q: Are the following graphs isomorphic? Justify..

A: We clearly see that the first graph, say G1 contains two 3-cycles [one the smaller inside and the…

Q: 8. The statistical measure that indicates how measured data vary from the given mean value of that…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Show that every group G of order n is isomorphic to a subgroup of Sn. (This is also called Caley's…

Q: Which set has higher cardinality: N or Z? Explain with example

A: Cardinality: The cardinality of a set A is the number of elements present in the set A. We denote…

Q: Find the projection of the function f(x) = cos2 x on the orthogonal set (1,cos x,cos 2x) on the…

Q: Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear sys…

Q: Use Cayley Hamilton theorem, the characteristic equation and A¹ of the matrix A = [3] -3 X²-4X+5=0.…

Q: Question 1 Which of the following sets of functions are linearly independent on (0, ∞)? O {1, tan²…

Q: Find the indicated nth partial sum of (Sn) if the arithmetic sequence. a) -3 + -3/2 + 0 +…+30 b) u2=…

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Find the general solution of the given differential equation. y' + 5x¹y = x4 y(x) = Give the largest…

A: Explanation of the answer is as follows

Q: Find the general solution of the given differential equation. cos(x) + (sin(x))y = 1 dx y(x) = Give…

A: Here we have to solve the given differential equation cos(x)dydx+sin(x)y=1 .

Q: Rewrite the following phrase utilising a solitary power series whose basic meaning includes…

Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

Q: Sow that 2 x² + y² + z² - c²t² is Lorentz invariant.

Q: find Fot the: f(t) = 35gh (3+) - let: 35gh (34) = 6 ju

A: What is Fourier Transformation: Integral transformations include Fourier transformations. It…

Q: Use finite approximations to estimate the area under the graph of the function f(x)=3−x2−2x between…

A: The Given function is, f(x)=3-x2-2x Between x=-3 and x=1 Here we have to find the area under the…

Q: Question 2 Use the slider to graph the standard position angle, then convert the degree to radians.…

A: Given Degree Measure = 176 degree

Q: Calculate the curvature and torsion for the following trajectories given by x(t) a(t) x + y(t) ŷ +…

Q: tions ge6fa02h.AP1-1.02 O ✪ O O O a. What is the mean price? Round your answer to the nearest cent.…

Q: Use the Rank method to test the consistency of the system of equations 3x + y + 2z = 3, 2x - 3y - z…

Q: (a) Use Gauss-Jordan method to find the inverse of the following matrix : [1 2 3] 567 87 0

Q: Verify that x and/ are solutions to the differential equation x²y" + xy - y = 0 on (0,00). Solve the…

Q: Find the general solution of the system whose augmented matrix is given below. 121 482-12 OA. Select…

Q: F.T. If X(t) + X(w) and X(W) = y(t) 71 ²-² (1-72)X = (1+2·1)1 (2+jwj2 find Yow) if

Q: Verify that the given differential equation is not exact. (-xy sin(x) + 2y cos(x)) dx + 2x cos(x) dy…

Q: What is the equation of the line that passes through the point (3, 10) and has slope 2, in…

A: The equation of the line passing through the point (a,b) with slope m, y-b =…

Q: a. b. C. List three points in 3-space which satisfy the Cartesian description: [x=2 \y = 5 Write a…

Q: Find the directional derivative of the scalar function of (x, y, z) = xyz in the direction of the…

A: What is Gradient of a Scalar Function: The gradient of a scalar function is vector quantity. It is…

Q: Find F.T the: f(x) = 1+ cos (6πt + I let: and 112T8 (W) Coswo- TT/S (W_W₁) + S (W+ wo) ]

Q: Problem 8: Prove that three dimentional volume element "dx dy dz" is not invariant butfour…

A: What is Lorentz Transformation: The Lorentz transformations are a family of linear transformations…

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

Q: For what value(s) of x is f(x) = 4?

A: The first thing we must do for this case is observed the y coordinates for a given value of x…

Q: If h:(R,+) → (R*,.) is a mapping defined by h(x)=10*, VXER, then (R,+) = (R*,.).

Q: Let T be a triangle with vertices (1,-2), (3,0), (-3,2), and f(x,y)=x^2(y-x+3) (a) Find the linear…

A: It is given that T is a triangle with vertices 1,-2, 3,0 and -3,2 and the function fx,y=x2y-x+3. (a)…

Q: (a) If 4-[a] is a 3x3 matrix; such that a -i (4-7), find the values of diagonal elements and the…

A: What is Matrix: If we arrange some elements, may be number or alphabets in rectangular array, the…

Q: For which parabola is the function f(x,y) Illustrate your answer. sin(xy) y-x² not defined?

Q: Find the LU factorization of A A= Ly To solve the system -2 -4 4 -7 4 -12 11 66 using the LU…

Q: 2. Analyze the solution to the following optimal growth model using a phase diagram drawn in (k, μ)…

A: Consider the given model, Vk0=max∫0∞e-ptlncdt subject to, k˙=k1-α1-α-c-δk, k0=k0, and kt≥0. So, for…

Q: The simple solid Q, drawn in the first octant and generated by the surfaces *See image 1*…

A: What is Three Dimensional Surface: A surface is a three dimensional figure. Therefore, in a surface,…

Q: Prove that if G is a graph of order p and has size greater than ¹) then G is connected. 2

Q: F.T. 3) If X(t) + y(t) = x (2t - 1) =it W+1 Ans: Yow) = [4+jCW+1)]² X(w) and X (w.) = -j(w+1) e 2…

Q: Decide whether the statement is true or false. Two set A and B are equal if have the same number of…

Q: integra

Q: 3. Form the partial differential equation by eliminating the arbitrary constants a and b from z = ď²…

Q: Show that SL(n, R) is a normal subgroup of GL(n, R). Further, by apply- ing Fundamental Theorem of…

A: Suppose, ϕ:GLn,R→R\0 such that ϕA=A for all A∈GLn,R Now, sinceA∈GLn,R if and only if A≠0 Now, we see…

Q: Let (X, T ) be a topological space, (M, d) be a complete metric space and BC(X, M) := {f ∈ C(X, M);…

A: Given as X,T be a topological space,M,d be a complete metric space and BCX,M=f∈CX,M;fX is bounded…

Q: find F.T the: f(t) = 35gh (3+) - let: 35gh (34) = T 6 jw

A: What is Fourier Transformation: Integral transformations include Fourier transformations. It…

Q: a) M = {1, 2}. Find the 4 topologies of M. b) Show that R^n\0 is connected only for n other than 1…

Q: Solve the BVP PDE: BCS: IC: u(x,0)=1,00 (0,1)=0, u(1,1)=0.1>0

A: What is Initial Boundary Value Problem: An initial boundary value problem is generally involved in…

Question

Let ̄f = c1φ1 + c2φ2 + ... + cnφn be the projection of f on the
orthogonal set (φ1,φ2,...φn). Show that f − ̄f is orthogonal to
each of the functions (φ1,φ2,...φn).

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).
10. Let and be mappings from to. Prove that if is invertible, then is onto and is one-to-one.
Let T be a linear transformation from R3 into R such that T(1,1,1)=1, T(1,1,0)=2 and T(1,0,0)=3. Find T(0,1,1)
27. Let , where and are nonempty. Prove that has the property that for every subset of if and only if is one-to-one. (Compare with Exercise 15 b.). 15. b. For the mapping , show that if , then .
Let T:R3R3 be the linear transformation that projects u onto v=(2,1,1). (a) Find the rank and nullity of T. (b) Find a basis for the kernel of T.
3. For each of the following mappings, write out and for the given and, where.
Consider the vectors u=(6,2,4) and v=(1,2,0) from Example 10. Without using Theorem 5.9, show that among all the scalar multiples cv of the vector v, the projection of u onto v is the closest to u that is, show that d(u,projvu) is a minimum.