/*! 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} Q37E 37. If A聽is a positive definit... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Q37E (page 414)

37. If Ais a positive definiten脳nmatrix andx鈫� is a nonzero vector inRn, then the angle betweenx鈫�andAx鈫�must be acute.

Short Answer

Expert verified

The given statement is TRUE.

Step by step solution

01

Check whether the given statement is TRUE or FALSE

Recall that if is the angle between two vectors x鈫�and y鈫�, then 0鈮�胃鈮�蟺and .

cos胃=y藱.y藱x藱y藱

If A is a positive definite, then x藱.Ax藱>0.

If the angle between them is 胃, then using the above formula, we get 肠辞蝉胃>0.

Here, 肠辞蝉胃is positive if 胃is acute and negative if 胃is obtuse. Hence, the angle between x藱and Ax藱is acute.

02

Final Answer

The given statement is TRUE.

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 the dimension of the spaceQ2 of all quadratic forms in two variables.

If Ais an invertible symmetric matrix, what is the relationship between the definiteness of A and A-1?

Diagonalize the13脳13matrix

[000鈥�01000鈥�01000鈥�01鈰�鈰�鈰�鈰�鈰�鈰�000鈥�01111鈰�11]

(All ones in the last row and the last column, and zeros elsewhere.)

Determine the definiteness of the quadratic forms in Exercises 4 through 7.

q(x1,x2)=x12+4x1x2+x22

LetU猢�0be a real upper triangularn脳n matrix with zeros on the diagonal. Show that

(ln+U)t猢�tn(ln+U+U2+.....+Un-1)

for all positive integers t. See Exercises 46 and 47.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

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.