/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q .18. Let v1聽and v2聽be two nonzero p... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Q .18. (page 812)

Let v1and v2be two nonzero position vectors in 鈩�2that are not scalar multiples of each other. Explain why, given any vector win 鈩�2, there are scalars c1and c2such that w=c1v1+c2v2.

Short Answer

Expert verified

There exists the scalarsc1andc2such thatw=c1v1+c2v2.

Step by step solution

01

Step 1:Given information

.v1andv2be two nonzero position vectors

02

Step 2:Explaination

The objective is to explain given any vectorwin鈩�2, there are scalarsc1andc2such that

w=c1v1+c2v2

The vectorsv1andv2in鈩�2are not the scalar multiple of each other. Thus, the vectors are

independent in鈩�2.

Thus, the vectorsv1andv2in鈩�2behave as basis of鈩�2

The space鈩�2is spanned by the vectorsv1andv2.

For any non-zero vectorwin鈩�2the vectorwis the linear combination of the vectorsv1andv2.

Thus, there exists the scalarsc1andc2such thatw=c1v1+c2v2.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Find PQ鈬赌

P=5,-3,Q=3,-6

What is the definition of the cross product?

A function f that satisfies the hypotheses of Rolle鈥檚 Theorem on [鈭�2, 2] and for which there are exactly three values c 鈭� (鈭�2, 2) that satisfy the conclusion of the theorem .

Calculate each of the limits:

limh鈫�011+h-1h.

In Exercises 20-23, find the dot product of the given pairs of vectors and the angle between the two vectors.

u=1,2,v=3,5
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.