Four MBA students take the same six courses at graduate business school. Their final marks in these courses are recorded (out of 100) in the matrix M = [m] where Page 9 of 10 the final mark in course j for MBA student i ow - Coulum mij = (a) State the matrices C and Q such that (i) the entries in the product MQ are the overall average final marks for cach student and (ii) the entrics in the product CM are the overall average final marks for each course. (b) State the matrix R such that the entries in the product RM represent a 5% increase in the final grades for all students in all courses. (c) Suppose the marks in M are altered as follows: the final mark for each student in Course #2 is reduced by 3 points, the final mark for each student in Course #5 is increased by 5 points, and all other marks remain unchanged. State the matrix K so that the sum K+ M has entries that reflect the alteration of the marks as described above.
Four MBA students take the same six courses at graduate business school. Their final marks in these courses are recorded (out of 100) in the matrix M = [m] where Page 9 of 10 the final mark in course j for MBA student i ow - Coulum mij = (a) State the matrices C and Q such that (i) the entries in the product MQ are the overall average final marks for cach student and (ii) the entrics in the product CM are the overall average final marks for each course. (b) State the matrix R such that the entries in the product RM represent a 5% increase in the final grades for all students in all courses. (c) Suppose the marks in M are altered as follows: the final mark for each student in Course #2 is reduced by 3 points, the final mark for each student in Course #5 is increased by 5 points, and all other marks remain unchanged. State the matrix K so that the sum K+ M has entries that reflect the alteration of the marks as described above.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 22EQ: Consider the matrix A=[2314]. Show that any of the three types of elementary row operations can be...
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![Four MBA students take the same six courses at graduate business school. Their
final marks in these courses are recorded (out of 100) in the matrix M = [m] where
Page 9 of 10
the final mark in course j for MBA student i ow
- Coulum
mij
=
(a) State the matrices C and Q such that (i) the entries in the product MQ are the overall
average final marks for cach student and (ii) the entrics in the product CM are the overall
average final marks for each course.
(b) State the matrix R such that the entries in the product RM represent a 5% increase in the
final grades for all students in all courses.
(c) Suppose the marks in M are altered as follows: the final mark for each student in Course
#2 is reduced by 3 points, the final mark for each student in Course #5 is increased by 5
points, and all other marks remain unchanged. State the matrix K so that the sum K + M
has entries that reflect the alteration of the marks as described above.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F14e5feb4-438d-4d91-8851-92fadf2e52c4%2F846458df-3e77-48df-b1e3-8a1e9d867742%2F8uus6id_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Four MBA students take the same six courses at graduate business school. Their
final marks in these courses are recorded (out of 100) in the matrix M = [m] where
Page 9 of 10
the final mark in course j for MBA student i ow
- Coulum
mij
=
(a) State the matrices C and Q such that (i) the entries in the product MQ are the overall
average final marks for cach student and (ii) the entrics in the product CM are the overall
average final marks for each course.
(b) State the matrix R such that the entries in the product RM represent a 5% increase in the
final grades for all students in all courses.
(c) Suppose the marks in M are altered as follows: the final mark for each student in Course
#2 is reduced by 3 points, the final mark for each student in Course #5 is increased by 5
points, and all other marks remain unchanged. State the matrix K so that the sum K + M
has entries that reflect the alteration of the marks as described above.
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