/*! 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} Q43E Determine whether the statements... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Q43E (page 40)

Determine whether the statements that follow are true or false, and justify your answer.

43.If two matrices A and B have the same reduced row-echelon form, then the equations Ax鈫�=0andBx鈫�=0 must have the same solutions.

Short Answer

Expert verified

The statement, 鈥淚f two matrices A and B have the same reduced row-echelon form, then the equations Ax鈫�=0andBx鈫�=0 must have the same solutions.鈥� is true.

Step by step solution

01

Consider the condition 

The number of leading in the reduced row-echelon form of a matrix determines the number of solutions. The number of leading 1's is equal to the number of solutions of the linear system of equations.

02

Conclusion

So, the matrices A and B have the same reduced row-echelon form. Thus, the equations Ax鈫�=0andBx鈫�=0 must have the same solutions.

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

Write the system in matrix form.

|x+2y+3z=14x+5y+6z=47x+8y+9z=9|

In exercises, 1 through 10, find all solutions of the linear systems using elimination.Then check your solutions.

8.x+2y+3z=04x+5y+6z=07x+8y+10z=0

Consider an n脳 mmatrix A, an r脳 smatrix B, and a vectorx鈫�in鈩�p. For which values of n, m, r,s, and pis the productA(Bx鈫�)defined?

Determine whether the statements that follow are true or false, and justify your answer.

16: There exists a 2脳2matrix such that

A[11]=[12]andA[22]=[21]

Consider a solutionx1鈫�of the linear systemAx鈫�=b鈫�. Justify the facts stated in parts (a) and (b):

a. Ifx鈫�his a solution of the systemAx鈫�=0鈫�, thenx1鈫�+xh鈫� is a solution of the systemA=x鈫�=b鈫�.

b. Ifx2鈫�is another solution of the systemAx鈫�=b鈫�, thenx1鈫�+xh鈫�is a solution of the system Ax鈫�+0鈫�.

c. Now suppose A is a2脳2matrix. A solution vectorx1鈫�of the systemAx鈫�+b鈫�is shown in the accompanying figure. We are told that the solutions of the systemAx鈫�=0鈫�form the line shown in the sketch. Draw the line consisting of all solutions of the systemAx鈫�=b鈫�.

If you are puzzled by the generality of this problem, think about an example first:

A=(1鈥呪赌呪赌呪赌�23鈥呪赌呪赌呪赌�6),b鈫�=[39]andx1鈫�=[11]
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

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.