Logout Open In App
Open In App
Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Chapter 1: Q44E (page 40)

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

44.If matrix E is in reduced row-echelon form, and if we omit a column of E, then the remaining matrix must be in the reduced row-echelon form as well.

Short Answer

Expert verified

Answer:

The statement, “If the matrix E is in reduced row-echelon form, and if we omit a column of E , then the remaining matrix must be in the reduced row-echelon form as well.” is false.

Step by step solution

01

Consider the condition

When a matrix is said to be in its reduced row-echelon form, then, it represents the number of solutions present in it.

If a column is removed, then, that matrix cannot be called to be in the reduced row-echelon form.

02

Conclusion

The matrix E is not said to be in the reduced row-echelon form, if one of the column is omitted.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

a. Using technology, generate a random 3×4 matrixA . (The entries may be either single-digit integers or numbers between 0and1 , depending on the technology you are using.) Find rref(A). Repeat this experiment a few times.

b. What does the reduced row-echelon form of most3×4 matrices look like? Explain.

The accompanying sketch represents a maze of one-way streets in a city in the United States. The traffic volume through certain blocks during an hour has been measured. Suppose that the vehicles leaving the area during this hour were exactly the same as those entering it.

What can you say about the traffic volume at the four locations indicated by a question mark? Can you figure out exactly how much traffic there was on each block? If not, describe one possible scenario. For each of the four locations, find the highest and the lowest possible traffic volume.

Students are buying books for the new semester. Brigitte buys the German grammar book and the German novel, Die Leiden des jungen Werther, forЄ64 in total. Claude spendsЄ98 on the linear algebra text and the German grammar book, while Denise buys the linear algebra text and Werther, for Є76. How much does each of the three books cost?

What are the signs of the determinants of the principal submatrices of a negative definite matrix? See Theorem 8.2.5.

Use the concept of a continuous dynamical system.Solve the differential equationdxdt=−kx. Solvethe system dx→dt=Ax→whenAis diagonalizable overR,and sketch the phase portrait for 2×2 matricesA.

Solve the initial value problems posed in Exercises 1through 5. Graph the solution.

4 .dydt=0.8twithy(0)=-0.8
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

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.

Sign-up for free