Mathematics All Around-Workbook
6th Edition
ISBN: 9780134462356
Author: Pirnot
Publisher: PEARSON
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Chapter 5.4, Problem 13E
To determine
To calculate:
The operation
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9.22 Develop, debug, and test a program in either a high-level language or a macro
language of your choice to solve a system of equations with Gauss-Jordan elimination
without partial pivoting. Base the program on the pseudocode from Fig. 9.10. Test the
program using the same system as in Prob. 9.18. Compute the total number of flops in
your algorithm to verify Eq. 9.37.
FIGURE 9.10
Pseudocode to implement the
Gauss-Jordan algorithm with-
out partial pivoting.
SUB GaussJordan(aug, m, n, x)
DOFOR k = 1, m
d = aug(k, k)
DOFOR j = 1, n
aug(k, j) = aug(k, j)/d
END DO
DOFOR 1 = 1, m
IF 1 % K THEN
d = aug(i, k)
DOFOR j = k, n
aug(1, j)
END DO
aug(1, j) - d*aug(k, j)
END IF
END DO
END DO
DOFOR k = 1, m
x(k) = aug(k, n)
END DO
END GaussJordan
11.9 Recall from Prob. 10.8, that the following system of equations
is designed to determine concentrations (the e's in g/m³) in a series
of coupled reactors as a function of amount of mass input to each
reactor (the right-hand sides are in g/day):
15c3cc33300
-3c18c26c3 = 1200
-4c₁₂+12c3 = 2400
Solve this problem with the Gauss-Seidel method to & = 5%.
9.8 Given the equations
10x+2x2-x3 = 27
-3x-6x2+2x3 = -61.5
x1 + x2 + 5x3 = -21.5
(a) Solve by naive Gauss elimination. Show all steps of the compu-
tation.
(b) Substitute your results into the original equations to check your
answers.
Chapter 5 Solutions
Mathematics All Around-Workbook
Ch. 5.1 - Write the Egyptian numerals using Hindu-Arabic...Ch. 5.1 - Write the Egyptian numerals using Hindu-Arabic...Ch. 5.1 - Prob. 3ECh. 5.1 - Write the Egyptian numerals using Hindu-Arabic...Ch. 5.1 - Write each Hindu-Arabic numeral using Egyptian...Ch. 5.1 - Write each Hindu-Arabic numeral using Egyptian...Ch. 5.1 - Prob. 7ECh. 5.1 - Write each Hindu-Arabic numeral using Egyptian...Ch. 5.1 - Prob. 9ECh. 5.1 - Perform each of the following addition problems...
Ch. 5.1 - Prob. 11ECh. 5.1 - Perform each of the following addition problems...Ch. 5.1 - Perform each of the following subtraction problems...Ch. 5.1 - Perform each of the following subtraction problems...Ch. 5.1 - Perform each of the following subtraction problems...Ch. 5.1 - Perform each of the following subtraction problems...Ch. 5.1 - Prob. 17ECh. 5.1 - Use the Egyptian method of doubling to calculate...Ch. 5.1 - Prob. 19ECh. 5.1 - Use the Egyptian method of doubling to calculate...Ch. 5.1 - Prob. 21ECh. 5.1 - Write each Roman numeral using Hindu-Arabic...Ch. 5.1 - Write each Roman numeral using Hindu-Arabic...Ch. 5.1 - Write each Roman numeral using Hindu-Arabic...Ch. 5.1 - Write each Roman numeral using Hindu-Arabic...Ch. 5.1 - Write each Roman numeral using Hindu-Arabic...Ch. 5.1 - Write each Roman numeral using Hindu-Arabic...Ch. 5.1 - Write each Roman numeral using Hindu-Arabic...Ch. 5.1 - Write each Roman numeral using Hindu-Arabic...Ch. 5.1 - Write each Roman numeral using Hindu-Arabic...Ch. 5.1 - Prob. 31ECh. 5.1 - Write each numeral in Roman notation There may be...Ch. 5.1 - Prob. 33ECh. 5.1 - Write each numeral in Roman notation There may be...Ch. 5.1 - Prob. 35ECh. 5.1 - Write each numeral in Roman notation There may be...Ch. 5.1 - Prob. 37ECh. 5.1 - Write each numeral in Roman notation There may be...Ch. 5.1 - Write each Chinese numeral as a Hindu-Arabic...Ch. 5.1 - Write each Chinese numeral as a Hindu-Arabic...Ch. 5.1 - Write each Chinese numeral as a Hindu-Arabic...Ch. 5.1 - Write each Chinese numeral as a Hindu-Arabic...Ch. 5.1 - Write each Chinese numeral as a Hindu-Arabic...Ch. 5.1 - Write each Chinese numeral as a Hindu-Arabic...Ch. 5.1 - Write each numeral using Chinese numerals. 495Ch. 5.1 - Write each numeral using Chinese numerals. 726Ch. 5.1 - Write each numeral using Chinese numerals. 2,805Ch. 5.1 - Write each numeral using Chinese numerals. 3,926Ch. 5.1 - Write each numeral using Chinese numerals. 9,846Ch. 5.1 - Write each numeral using Chinese numerals. 8,054Ch. 5.1 - The Great Pyramid at Giza was completed in . Write...Ch. 5.1 - Cheops, the builder of the Great Pyramid at Giza,...Ch. 5.1 - An Egyptian merchant has a warehouse that contains...Ch. 5.1 - An ancient Egyptian merchant had on hand bushels...Ch. 5.1 - Using Egyptian notation, the number 100,...Ch. 5.1 - Using Egyptian notation, the number 100,...Ch. 5.1 - Using Egyptian notation, the number 100,...Ch. 5.1 - Using Egyptian notation, the number 100,...Ch. 5.1 - The emperor Aurelius Constantine, who lived from...Ch. 5.1 - By 285ad, the Roman Empire had become so vast that...Ch. 5.1 - Frequently, Roman numerals are used today in movie...Ch. 5.1 - Prob. 62ECh. 5.1 - Prob. 63ECh. 5.1 - Frequently, Roman numerals are used today in movie...Ch. 5.1 - The counting boards In Exercises 6568 show...Ch. 5.1 - The counting boards In Exercises 6568 show...Ch. 5.1 - The counting boards In Exercises 6568 show...Ch. 5.1 - The counting boards In Exercises 6568 show...Ch. 5.1 - The oldest discovery of Chinese written numerals...Ch. 5.1 - When Marco Polo visited China in 1274, he was...Ch. 5.1 - Explain two advantages of the Roman numeration...Ch. 5.1 - The Roman numeration system has symbols for 5,50,...Ch. 5.1 - The traditional Chinese numeration system had no...Ch. 5.1 - Research the Ionic Greek numeration system, which...Ch. 5.1 - In the Egyptian numeration system, whenever we...Ch. 5.1 - Suppose that Egyptian numeration was based on 5...Ch. 5.1 - Invent an Egyptian type of numeration system using...Ch. 5.1 - Write the number 1,999 in Roman numerals in as...Ch. 5.1 - Egyptian mathematics had a unique way of writing...Ch. 5.1 - Egyptian mathematics had a unique way of writing...Ch. 5.1 - Egyptian mathematics had a unique way of writing...Ch. 5.1 - Egyptian mathematics had a unique way of writing...Ch. 5.2 - Write the following Babylonian numerals as...Ch. 5.2 - Write the following Babylonian numerals as...Ch. 5.2 - Write the following Babylonian numerals as...Ch. 5.2 - Write the following Babylonian numerals as...Ch. 5.2 - Write each number using Babylonian notation. 8,235Ch. 5.2 - Write each number using Babylonian notation. 7,331Ch. 5.2 - Write each number using Babylonian notation....Ch. 5.2 - Write each number using Babylonian notation....Ch. 5.2 - Write each number using Babylonian notation....Ch. 5.2 - Write each number using Babylonian notation....Ch. 5.2 - Write each number using Babylonian notation....Ch. 5.2 - Write each number using Babylonian notation....Ch. 5.2 - Translate each of the following Mayan numerals to...Ch. 5.2 - Translate each of the following Mayan numerals to...Ch. 5.2 - Translate each of the following Mayan numerals to...Ch. 5.2 - Translate each of the following Mayan numerals to...Ch. 5.2 - Write each number using Mayan notation. 17Ch. 5.2 - Write each number using Mayan notation. 48Ch. 5.2 - Prob. 19ECh. 5.2 - Prob. 20ECh. 5.2 - Prob. 21ECh. 5.2 - Prob. 22ECh. 5.2 - Prob. 23ECh. 5.2 - Prob. 24ECh. 5.2 - Prob. 25ECh. 5.2 - Prob. 26ECh. 5.2 - Prob. 27ECh. 5.2 - Prob. 28ECh. 5.2 - Prob. 29ECh. 5.2 - Prob. 30ECh. 5.2 - Prob. 31ECh. 5.2 - Prob. 32ECh. 5.2 - Prob. 33ECh. 5.2 - Prob. 34ECh. 5.2 - Prob. 35ECh. 5.2 - Prob. 36ECh. 5.2 - Prob. 37ECh. 5.2 - Prob. 38ECh. 5.2 - Prob. 39ECh. 5.2 - Prob. 40ECh. 5.2 - Prob. 41ECh. 5.2 - Prob. 42ECh. 5.2 - Prob. 43ECh. 5.2 - Prob. 44ECh. 5.2 - Prob. 45ECh. 5.2 - Prob. 46ECh. 5.2 - Prob. 47ECh. 5.2 - Prob. 48ECh. 5.2 - Prob. 49ECh. 5.2 - Prob. 50ECh. 5.2 - Prob. 51ECh. 5.2 - Prob. 52ECh. 5.2 - Prob. 53ECh. 5.2 - Prob. 54ECh. 5.2 - Prob. 55ECh. 5.2 - Prob. 56ECh. 5.2 - Prob. 57ECh. 5.2 - Prob. 58ECh. 5.2 - Prob. 59ECh. 5.2 - Prob. 60ECh. 5.2 - Prob. 61ECh. 5.2 - Prob. 62ECh. 5.2 - Prob. 63ECh. 5.2 - Prob. 64ECh. 5.2 - Prob. 65ECh. 5.2 - Prob. 66ECh. 5.2 - Prob. 67ECh. 5.2 - Prob. 68ECh. 5.2 - Prob. 69ECh. 5.2 - Prob. 70ECh. 5.2 - Prob. 71ECh. 5.2 - Prob. 72ECh. 5.2 - Prob. 73ECh. 5.2 - Prob. 74ECh. 5.2 - Prob. 75ECh. 5.2 - Prob. 76ECh. 5.2 - Prob. 77ECh. 5.2 - Prob. 78ECh. 5.2 - Prob. 79ECh. 5.2 - Prob. 80ECh. 5.3 - Prob. 1ECh. 5.3 - Prob. 2ECh. 5.3 - Prob. 3ECh. 5.3 - Prob. 4ECh. 5.3 - Prob. 5ECh. 5.3 - Prob. 6ECh. 5.3 - Prob. 7ECh. 5.3 - Prob. 8ECh. 5.3 - Prob. 9ECh. 5.3 - Prob. 10ECh. 5.3 - Prob. 11ECh. 5.3 - Prob. 12ECh. 5.3 - Prob. 13ECh. 5.3 - Prob. 14ECh. 5.3 - Prob. 15ECh. 5.3 - Prob. 16ECh. 5.3 - Prob. 17ECh. 5.3 - Prob. 18ECh. 5.3 - Prob. 19ECh. 5.3 - Prob. 20ECh. 5.3 - Prob. 21ECh. 5.3 - Prob. 22ECh. 5.3 - Prob. 23ECh. 5.3 - Prob. 24ECh. 5.3 - Prob. 25ECh. 5.3 - Prob. 26ECh. 5.3 - Prob. 27ECh. 5.3 - Prob. 28ECh. 5.3 - Prob. 29ECh. 5.3 - Prob. 30ECh. 5.3 - Prob. 31ECh. 5.3 - Prob. 32ECh. 5.3 - Prob. 33ECh. 5.3 - Prob. 34ECh. 5.3 - Prob. 35ECh. 5.3 - Prob. 36ECh. 5.3 - Prob. 37ECh. 5.3 - Prob. 38ECh. 5.3 - Prob. 39ECh. 5.3 - Prob. 40ECh. 5.3 - Prob. 41ECh. 5.3 - Prob. 42ECh. 5.3 - Prob. 43ECh. 5.3 - Prob. 44ECh. 5.3 - Prob. 45ECh. 5.3 - Prob. 46ECh. 5.3 - Prob. 47ECh. 5.3 - Prob. 48ECh. 5.3 - Prob. 49ECh. 5.3 - Prob. 50ECh. 5.3 - Prob. 51ECh. 5.3 - Prob. 52ECh. 5.3 - Prob. 53ECh. 5.3 - Prob. 54ECh. 5.3 - Prob. 55ECh. 5.3 - Prob. 56ECh. 5.3 - Prob. 57ECh. 5.3 - Prob. 58ECh. 5.3 - Prob. 59ECh. 5.3 - Prob. 60ECh. 5.3 - Prob. 61ECh. 5.3 - Prob. 62ECh. 5.3 - Prob. 63ECh. 5.3 - Prob. 64ECh. 5.3 - Prob. 65ECh. 5.3 - Prob. 66ECh. 5.3 - Prob. 67ECh. 5.3 - Prob. 68ECh. 5.3 - Prob. 69ECh. 5.3 - Prob. 70ECh. 5.3 - Prob. 71ECh. 5.3 - Prob. 72ECh. 5.3 - Prob. 73ECh. 5.3 - Prob. 74ECh. 5.3 - Prob. 75ECh. 5.3 - Prob. 76ECh. 5.3 - Prob. 77ECh. 5.3 - Prob. 78ECh. 5.3 - Prob. 79ECh. 5.3 - Prob. 80ECh. 5.3 - Prob. 81ECh. 5.3 - Prob. 82ECh. 5.3 - Prob. 83ECh. 5.3 - Prob. 84ECh. 5.3 - Prob. 85ECh. 5.3 - Prob. 86ECh. 5.3 - Prob. 87ECh. 5.3 - Prob. 88ECh. 5.3 - Prob. 89ECh. 5.3 - Prob. 90ECh. 5.3 - Prob. 91ECh. 5.3 - Prob. 92ECh. 5.3 - Prob. 93ECh. 5.3 - Prob. 94ECh. 5.3 - Prob. 95ECh. 5.3 - Prob. 96ECh. 5.3 - Prob. 97ECh. 5.3 - Prob. 98ECh. 5.3 - Prob. 99ECh. 5.3 - Prob. 100ECh. 5.3 - Prob. 101ECh. 5.3 - Prob. 102ECh. 5.4 - Prob. 1ECh. 5.4 - Prob. 2ECh. 5.4 - Prob. 3ECh. 5.4 - Prob. 4ECh. 5.4 - Prob. 5ECh. 5.4 - Prob. 6ECh. 5.4 - Prob. 7ECh. 5.4 - Prob. 8ECh. 5.4 - Prob. 9ECh. 5.4 - Prob. 10ECh. 5.4 - Prob. 11ECh. 5.4 - Prob. 12ECh. 5.4 - Prob. 13ECh. 5.4 - Prob. 14ECh. 5.4 - Prob. 15ECh. 5.4 - Prob. 16ECh. 5.4 - Prob. 17ECh. 5.4 - Prob. 18ECh. 5.4 - Prob. 19ECh. 5.4 - Prob. 20ECh. 5.4 - Prob. 21ECh. 5.4 - Prob. 22ECh. 5.4 - Prob. 23ECh. 5.4 - Prob. 24ECh. 5.4 - Prob. 25ECh. 5.4 - Prob. 26ECh. 5.4 - Prob. 27ECh. 5.4 - Prob. 28ECh. 5.4 - Prob. 29ECh. 5.4 - Prob. 30ECh. 5.4 - Prob. 31ECh. 5.4 - Prob. 32ECh. 5.4 - Prob. 33ECh. 5.4 - Prob. 34ECh. 5.4 - Prob. 35ECh. 5.4 - Prob. 36ECh. 5.4 - Prob. 37ECh. 5.4 - Prob. 38ECh. 5.4 - Prob. 39ECh. 5.4 - Prob. 40ECh. 5.4 - Prob. 41ECh. 5.4 - Prob. 42ECh. 5.4 - Prob. 43ECh. 5.4 - Prob. 44ECh. 5.4 - Prob. 45ECh. 5.4 - Prob. 46ECh. 5.4 - Prob. 47ECh. 5.4 - Prob. 48ECh. 5.4 - Prob. 49ECh. 5.4 - Prob. 50ECh. 5.4 - Prob. 51ECh. 5.4 - Prob. 52ECh. 5.4 - Prob. 53ECh. 5.4 - Prob. 54ECh. 5.4 - Prob. 55ECh. 5.4 - Prob. 56ECh. 5.4 - a. Why are check digits important? Give an...Ch. 5.4 - Prob. 58ECh. 5.4 - Prob. 59ECh. 5.4 - Prob. 60ECh. 5.4 - Prob. 61ECh. 5.4 - Prob. 62ECh. 5.4 - Prob. 63ECh. 5.4 - Challenge Yourself When we do usual division of...Ch. 5.4 - Prob. 65ECh. 5.CR - Prob. 1CRCh. 5.CR - Prob. 2CRCh. 5.CR - Prob. 3CRCh. 5.CR - Prob. 4CRCh. 5.CR - Prob. 5CRCh. 5.CR - Prob. 6CRCh. 5.CR - Prob. 7CRCh. 5.CR - Prob. 8CRCh. 5.CR - Prob. 9CRCh. 5.CR - Prob. 10CRCh. 5.CR - Prob. 11CRCh. 5.CR - Prob. 12CRCh. 5.CR - Prob. 13CRCh. 5.CR - Prob. 14CRCh. 5.CR - Prob. 15CRCh. 5.CR - Prob. 16CRCh. 5.CR - Prob. 17CRCh. 5.CR - Prob. 18CRCh. 5.CR - Prob. 19CRCh. 5.CR - Prob. 20CRCh. 5.CR - Prob. 21CRCh. 5.CR - Prob. 22CRCh. 5.CR - Prob. 23CRCh. 5.CT - Write 3,685 in Roman notation.Ch. 5.CT - Prob. 2CTCh. 5.CT - Write 2647 and A3E16 as base-10 numerals.Ch. 5.CT - Prob. 4CTCh. 5.CT - Prob. 5CTCh. 5.CT - Prob. 6CTCh. 5.CT - Prob. 7CTCh. 5.CT - Prob. 8CTCh. 5.CT - Prob. 9CTCh. 5.CT - Prob. 10CTCh. 5.CT - Prob. 11CTCh. 5.CT - Prob. 12CTCh. 5.CT - Prob. 13CTCh. 5.CT - Prob. 14CTCh. 5.CT - Prob. 15CTCh. 5.CT - Prob. 16CTCh. 5.CT - Prob. 17CTCh. 5.CT - Prob. 18CTCh. 5.CT - Prob. 19CTCh. 5.CT - Prob. 20CTCh. 5.CT - Prob. 21CTCh. 5.CT - Prob. 22CT
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