Question: Show that |u + v| |u| + |v| for any vectors u and v.

Show that |u + v| ≤ |u| + |v| for any vectors u and v.

Step by Step Solution

★★★★★

3.40 Rating (163 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Let u and v be any two vectors By the triangle inequality for vectors we have ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

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

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Precalculus Questions!

Q:

Let U and W be subspaces of V (a) Show that U + W is a subspace of V containing U and W. (b) Show that span {u, w} = Ru + Rw for any vectors u and w. (c) Show that span {u1,...um, w1...,wn} = span{u1...

Q:

The cross product between vectors in R3 is defined by the formula Where (a) Show that u = v à w is orthogonal, under the dot product, to both v and w. (b) Show that v à w = 0 if and...

Q:

The definition u v = |u| |v| cos implies that |u v| |u||v| (because |cos | 1). This inequality, known as the CauchySchwarz Inequality, holds in any number of dimensions and has many...

Q:

Assignment 1 Deadline: 2023-02-07 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 1. Let u = [u1,...

Q:

Let u and v be two non-zero vectors in R" represented by directed line segments in standard position as in the diagram below. These can be viewed as two sides of a parallelogram. da de (a) (1 mark)...

Q:

I need help with this question and do it carefully so that i can understand it. 17. Show that u, v, and w are all in the span(u, v, w) 18. Determine if the given vectors are linearly independent 19....

Q:

6.05 Lens and Mirror Lab Templat X 6.06 Snell's Law Template - Goog X *Search Results | Course Hero X 19 Exam: 08.09 Segment Two Exam | X X C ^...

Q:

Let u, v and w be the vectors in R given by u = 5[0, -2, 5] + 4[-1, -1, 1], v= 5[0, -2, 5] - 3[-1, -1, 1], and w = -7u + 5v. Write w as a linear combination of [0, -2, 5] and [-1, -1, 1]. W= [0, -2,...

Q:

only do 9 please explain it with steps (b) Prove that if F has characteristic two, then S is linearly dependent. 9. Let u and v be distinct vectors in a vector space V. Show that {u, v} is linearly...

Q:

please explain it with steps 9. Let u and v be distinct vectors in a vector space V. Show that {u, v} is linearly dependent if and only if u or v is a multiple of the other. 10. Give an example of...

Q:

Answer Exercise 7.4.7 when L = 3D2 - 2D - 5. Exercise 7.4.7 Define L[y] = y" + y. (a) Prove directly from the definition that L: C2[a, b] C0[a, b] is a linear transformation. (b) Determine ker L.

Q:

Retained earnings can take the form of a. cash b. accounts recievable c. inventory d. all of the above

Q:

If you had to choose one gland and / or resulting hormone to live without, which one would it be and why?

Q:

This chapter describes both off the shelf and end user programming as types of applications. Discuss what is meant by these terms and provide some examples of each.

Q:

Find the derivative of the vector function. r(t) = a + t b + t 2 c

Q:

Find the derivative of the vector function. r(t) = t a x (b + t c)

Q:

Find the unit tangent vector T(t) at the point with the given value of the parameter t. r(t) = (t 2 - 2t, 1 + 3t, 1/3 t 3 + 1/2t 2 ) , t = 2

Q:

Exercise 15-4 Analysis of cost flows L.O. C2, P1, P2, P3 As of the end of June, the job cost sheets at Racing Wheels, Inc., show the following total costs accumulated on three custom jobs. Job 102...

Q:

Holland, Flowers, and Tulip have been partners while sharing net income and loss in a 5:3:2 ratio. On January 31, the date Tulip retires from the partnership, the equities of the partners are...

Q:

sales budget for next month of $600,000. COGS is expected to be 30 % of sales. All goods are purchased in the month used and paid for in the month following purchase. The beginning inventory of...