/*! 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.6.1-46E There exists a real number聽 suc... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q.6.1-46E (page 276)

There exists a real number such that the matrix

[123456k789870065]Is invertible. .

Short Answer

Expert verified

Therefore,

K=3252 and it is invertible

So, the given statement is true.

Step by step solution

01

Matrix Definition

Matrix is aset of numbers arranged in rows and columns so as to form a rectangulararray.

The numbers are called the elements, or entries, of the matrix.

If there are m rows and n columns, the matrix is said to be a 鈥� m by n鈥� 'matrix, written 鈥� m脳n鈥�.

02

Given

Given matrix,

A=123456k789870065


03

To check whether the given condition is true or false 

We compute

detA=-6.124567897+5.12356k898

A=-6路9+5路(7k-41)A=35k-259

So, for example, A is invertible for k=3252.

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

Vandermonde determinants (introduced by Alexandre-Th茅ophile Vandermonde). Consider distinct real numbers a0,a1,.....,an.. We define(n+1)脳(n+1) the matrix

A=[11....1a0a1....ana02a12....a12a0na1n....ann]

Vandermonde showed that

det(A)=鈭�i>j(ai-aj)

the product of all differences(ai-aj), where exceeds j.
a. Verify this formula in the case ofn=1.
b. Suppose the Vandermonde formula holds forn=1. You are asked to demonstrate it for n. Consider the function

f(t)=det[11...11a0a1...an-1ta02a12...an-1t2鈰�鈰�...鈰�鈰�a0na1n...an-1ntn]

Explain why f(t) is a polynomial of nthdegree. Find the coefficient k oftn using Vandermonde's formula fora0,...,an-1. Explain why

role="math" localid="1659522435181" f(a0)=f(a1)=...=f(an-1)=0

Conclude that

f(t)=k(t-a0)(t-a1)...(t-an-1)

for the scalar k you found above. Substitutet=an to demonstrate Vandermonde's formula.

An8脳8matrix fails to be invertible if (and only if) its determinant is nonzero.

In Exercises 5 through 40, find the matrix of the given linear transformation with respect to the given basis. If no basis is specified, use standard basis:for,

forandfor,.For the spaceof upper triangularmatrices, use the basis

Unless another basis is given. In each case, determine whetheris an isomorphism. Ifisn鈥檛 an isomorphism, find bases of the kernel and image ofand thus determine the rank of.

21. from to with respect to the basis.

IfA is a 4脳4 matrix whose entries are all 1 or -1 , then detAmust be divisible by 8 (i.e., detA=8kfor some integer k).

If is any noninvertible square matrix, then detA=det(rrefA).
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Applied 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.