Question: Using mathematical induction, prove the following generalization of the Triangle Inequality: ||v1 + v2 + + vn || || v1 || + ||

Using mathematical induction, prove the following generalization of the Triangle Inequality:
||v1 + v2 + ∙∙∙∙ + vn || ≤ || v1 || + || v2 || + ∙∙∙ + || vn || for all n ≥ 1

Step by Step Solution

★★★★★

3.37 Rating (163 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The basis for induction is the cases n 1 and n 2 The n 1 case is the a... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

859-L-A-L-S (2168).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Prove the following generalization of Theorem 7.3: If X1, X2, . . ., and Xn are independent random variables and Y = a1X1 + a2X2 + · · · + anXn, then Where MXi(t) is the value of...

Prove the following generalization of Theorem 4.5.6: For any random vector (X1,. . . . . . ., Xn) (. Va , |-w X+2 Cov(X, , X ). Isicjsn

Recall that a function g : I (open interval) ( ( ( is said to be convex if g(a1x1 + a2x2) ( a1g(x1) + a2g(x2) for all a1, a2 ( 0 with a1 + a2 = 1, and all x1, x2 ( I. Prove the following...

Proofs and Programming 1 . Consider the language of all strings over S = { a , b } that contain exactly twice as many occurrences of a as occurrences of b . The strings aab aba aabbaa would all be in...

4 This assignment, based on the content of Unit 4 of the Study Guide, is worth 3% of your grade. We recommend that you hand it in after you complete Unit 4. You must show all of your work in order to...

Consider the following definitions: Definition The set of linked lists of natural numbers L is defined by: Basis Step: EL Recursive Step: If I EL and n E N, then (n.) EL Definition The function...

Name: _______________ LoE: ______ hours ECE 3054 Homework 01 Fall 2017 This particular homework assignment is not typical of the assignments in this course, because it is intended to test your...

Consider the following sum Sn: Sn = V1 + V2 + ... + Vn. (i) From the theory in class, lower and upper bounds on Sn can be obtained by using the following formula with some function f(x). S f(x)dxss....

Thank you! Will give thumbs up! 6. (10 pts)) Consider the following sum Sn: S. = V1 + V2 + ... + Vn. (1) (3 pts) From the theory in class, lower and upper bounds on S, can be obtained by using the...

Consider the system described by the following differential equation: d2y dt2 3 dy dt 2y u (1) In this problem, we are interested in the solution to the associated homogeneous equation, i.e. set uptq...

How would a telecommunications company use activity-based costing in conducting profit analysis?

For a random sample of 36 items and a sample mean of 211, compute a 95% confidence interval for if the population standard deviation is 23. Round the answers to 2 decimal places.

Cu l de los siguientes polimeros previene la desecaci n del cigoto en carofitas? Celulosa Lignina Esporopolenina Almid n

Beth is a project manager for her organization. Management has asked Beth to use the CPM approach in her network diagram. She is not familiar with this approach and shes asked you to help her...

A linear transformation T : V V is given. If possible, find a basis C for V such that the matrix [T] c of T with respect to C is diagonal. T : P 1 P 1 defined by T(p(x)) = p(x) + xp(x)

If C is an (n, k) linear code that is self dual, prove that n must be even. [Use the analogue in Z n 2 of Theorem 5.13.]

A linear transformation T : V V is given. If possible, find a basis C for V such that the matrix [T] c of T with respect to C is diagonal. T : P 2 P 2 defined by T(p(x)) = p(x + 1)

Question 1 0 ( 2 points ) { ( a b ) 3 n : n 0 } is not a regular language. True False Question 1 1 ( 4 points ) To which regular set the following regular expression corresponds to . ( a a b b ) * a...

Of 54 bank customers depositing a check, 23 received some cash back. (a) Construct a 90 percent confidence interval for the proportion of all depositors who ask for cash back. (Round your answers to...

Give the degrees of freedom for the chisquare test based on the two-way table. E F G Total A 3'? 34 43 34 150 3 F5 85' 3\"] 5'3 330 C 23 3? 27 33 120 Total 140 160 140 160 600 Degrees of freedom = n