Explanation Given: The multiplicative inverse A − 1 is [ 0 0 1 0 1 0 1 0 0 ] . Procedure used: “ Multiplicative inverse of matrix C by Gauss-Jordon elimination , Step 1 : Form the augmented matrix of given matrix as [ C | I n ] , where I n is the multiplicative identity matrix of the same order as the given matrix C . Step 2 : Perform row operations on [ C | I n ] to obtain a matrix in the form of [ I n | B ] . Step 3 : The Matrix B obtained in Step 2 is C − 1 . Step 4 : Verify the result C C − 1 = I n and C − 1 C = I n .” Calculation: The multiplicative inverse A − 1 is [ 0 0 1 0 1 0 1 0 0 ] and the identity matrix I 3 is [ 1 0 0 0 1 0 0 0 1 ] . Consider the above matrix A − 1 as matrix C as follows: C = [ 0 0 1 0 1 0 1 0 0 ] ( 1 ) Step 1: Form the augmented matrix in the form of [ C | I 3 ] . [ 0 0 1 1 0 0 0 1 0 0 1 0 1 0 0 0 0 1 ] Step 2: Perform row operations on augmented matrix as follows: Apply ( R 1 ↔ R 3 ) in the above matrix. [ 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 ] Therefore, the above expression is in the form of [ I 3 | B ] . Step 3: The matrix on Left Hand Side is Identity ( I 3 ) and on Right Hand Side is matrix B . Therefore, Matrix B is C − 1 . Therefore, the multiplicative inverse C − 1 is [ 0 0 1 0 1 0 1 0 0 ] . Step 4: The verification of C C − 1 = I 3 is given below: The Left hand side C C − 1 is calculated as follows: C C − 1 = [ 0 0 1 0 1 0 1 0 0 ] [ 0 0 1 0 1 0 1 0 0 ] = [ ( 0 ) ( 0 ) + ( 0 ) ( 0 ) + ( 1 ) ( 1 ) ( 0 ) ( 0 ) + ( 0 ) ( 1 ) + ( 1 ) ( 0 ) ( 0 ) ( 1 ) + ( 0 ) ( 0 ) + ( 1 ) ( 0 ) ( 0 ) ( 0 ) + ( 1 ) ( 0 ) + ( 0 ) ( 1 ) ( 0 ) ( 0 ) + ( 1 ) ( 1 ) + ( 0 ) ( 0 ) ( 0 ) ( 1 ) + ( 1 ) ( 0 ) + ( 0 ) ( 0 ) ( 1 ) ( 0 ) + ( 0 ) ( 0 ) + ( 0 ) ( 1 ) ( 1 ) ( 0 ) + ( 0 ) ( 1 ) + ( 0 ) ( 0 ) ( 1 ) ( 1 ) + ( 0 ) ( 0 ) + ( 0 ) ( 0 ) ] = [ 0 + 0 + 1 0 + 0 + 0 0 + 0 + 0 0 + 0 + 0 0 + 1 + 0 0 + 0 + 0 0 + 0 + 0 0 + 0 + 0 1 + 0 + 0 ] = [ 1 0 0 0 1 0 0 0 1 ] The Right Hand Side I 3 is as follows: I 3 = [ 1 0 0 0 1 0 0 0 1 ] Therefore, Left Hand Side C C − 1 is equal to Right Hand Side Identity matrix I 3

A Graphical Approach to College Algebra, Books a la Carte Edition (6th Edition)

6th Edition

ISBN: 9780321900715

Author: John Hornsby, Margaret L. Lial

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 6.6, Problem 64E

To determine

The matrix A if the multiplicative inverse is A−1=[001010100].

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.6, Problem 63E

Chapter 6.6, Problem 65E

Students have asked these similar questions

Compare the interest earned from #1 (where simple interest was used) to #5 (where compound interest was used). The principal, annual interest rate, and time were all the same; the only difference was that for #5, interest was compounded quarterly. Does the difference in interest earned make sense? Select one of the following statements. a. No, because more money should have been earned through simple interest than compound interest. b. Yes, because more money was earned through simple interest. For simple interest you earn interest on interest, not just on the amount of principal. c. No, because more money was earned through simple interest. For simple interest you earn interest on interest, not just on the amount of principal. d. Yes, because more money was earned when compounded quarterly. For compound interest you earn interest on interest, not just on the amount of principal.

Compare and contrast the simple and compound interest formulas. Which one of the following statements is correct? a. Simple interest and compound interest formulas both yield principal plus interest, so you must subtract the principal to get the amount of interest. b. Simple interest formula yields principal plus interest, so you must subtract the principal to get the amount of interest; Compound interest formula yields only interest, which you must add to the principal to get the final amount. c. Simple interest formula yields only interest, which you must add to the principal to get the final amount; Compound interest formula yields principal plus interest, so you must subtract the principal to get the amount of interest. d. Simple interest and compound interest formulas both yield only interest, which you must add to the principal to get the final amount.

Sara would like to go on a vacation in 5 years and she expects her total costs to be $3000. If she invests $2500 into a savings account for those 5 years at 8% interest, compounding semi-annually, how much money will she have? Round your answer to the nearest cent. Show you work. Will she be able to go on vacation? Why or why not?

Chapter 6 Solutions

A Graphical Approach to College Algebra, Books a la Carte Edition (6th Edition)

Ch. 6.1 - CHECKING ANALYTIC SKILLS Use each graph to...Ch. 6.1 - Prob. 8E Ch. 6.1 - CHECKING ANALYTIC SKILLS Use each graph to...Ch. 6.1 - Prob. 10E Ch. 6.1 - Prob. 11E Ch. 6.1 - Prob. 12E Ch. 6.1 - Prob. 13E Ch. 6.1 - Prob. 14E Ch. 6.1 - Prob. 15E Ch. 6.1 - Prob. 16E

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

The matrix A if the multiplicative inverse is A − 1 = [ 0 0 1 0 1 0 1 0 0 ] .

Videos

The matrix A if the multiplicative inverse is A−1=[001010100].

Want to see the full answer?

Chapter 6 Solutions