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Example 22 Matrix B shows the number of sightings of rare birds made by members of a birdwatching club. B= Harry Esther Aniela Cordon Flitter Bitwing Redtwit 13 3 25 2 1 1 E 7 10 423 3 -A P=[1111] Q=

Example 22 Matrix B shows the number of sightings of rare birds made by members of a birdwatching club. B= Harry Esther Aniela Cordon Flitter Bitwing Redtwit 13 3 25 2 1 1 E 7 10 423 3 -A P=[1111] Q=

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Example 22 Matrix B shows the number of sightings of rare birds made by members of a birdwatching club. B = a b C Harry Esther Aniela Gordon Flitter 2 13 ii Bitwing Redtwit 3 4 2 5 2 1 1 3 5 7 10 P=[ 1 [] [] 1] i Calculate the product A = PB. What information does the element a13 give? Calculate C BQ and describe the information given by C. ii What information does the element C₂1 give? 1 Calculate PBQ and describe the information given by this matrix. 14 | Page
Transcribed Image Text:Example 22 Matrix B shows the number of sightings of rare birds made by members of a birdwatching club. B = a b C Harry Esther Aniela Gordon Flitter 2 13 ii Bitwing Redtwit 3 4 2 5 2 1 1 3 5 7 10 P=[ 1 [] [] 1] i Calculate the product A = PB. What information does the element a13 give? Calculate C BQ and describe the information given by C. ii What information does the element C₂1 give? 1 Calculate PBQ and describe the information given by this matrix. 14 | Page
Example23 WEB A supermarket has three types of apples priced at $2.50, $3.50 and $4.00 per kilogram and three types of avocados priced at $0.90, $1.90 and $2.50. The manager wishes to mark up the prices of the avocados by 15% and mark down the prices of the apples by 15%. a Show the prices of the apples and avocados as a suitable matrix. b Show the matrix obtained by marking down the prices of the apples by 15% and marking up the prices of the avocados by 15%. c Use matrix multiplication to calculate the new prices (to the nearest cent). Example 24 Four students A, B, C, and D each completed 3 maths tests. Their results are shown in matrix R. The test marks were not equally weighted in determining the final grade. To work out a final grade, test 1 was worth 50%, test 2 was worth 20% and test 3 30%. RO A B C D 72 33 59 82 83 67 58 94 70 80 42 55 a) State a 1 x 3 matrix P, which shows the percentages each test is worth as a decimal. b) Determine PR and interpret
Transcribed Image Text:Example23 WEB A supermarket has three types of apples priced at $2.50, $3.50 and $4.00 per kilogram and three types of avocados priced at $0.90, $1.90 and $2.50. The manager wishes to mark up the prices of the avocados by 15% and mark down the prices of the apples by 15%. a Show the prices of the apples and avocados as a suitable matrix. b Show the matrix obtained by marking down the prices of the apples by 15% and marking up the prices of the avocados by 15%. c Use matrix multiplication to calculate the new prices (to the nearest cent). Example 24 Four students A, B, C, and D each completed 3 maths tests. Their results are shown in matrix R. The test marks were not equally weighted in determining the final grade. To work out a final grade, test 1 was worth 50%, test 2 was worth 20% and test 3 30%. RO A B C D 72 33 59 82 83 67 58 94 70 80 42 55 a) State a 1 x 3 matrix P, which shows the percentages each test is worth as a decimal. b) Determine PR and interpret
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