aiShot(购买解锁去水印) The public health authorities of a small town have divided the population into three categories: covid- negative, covid-positive, and hospitalised. After performing regular, extensive tests, they have observed that in each successive week: • Among those who are negative, 95% remain so, 4% become positive, and 1% need to be hospitalised. • Among those who are positive, 75% recover and become negative, 20% stay positive, and 5% need to be hospitalised. • Among those who are hospitalised, 60% recover and become negative, 30% are released from hospital but remain positive, and 10% remain hospitalised. (a) After representing the population in a given week as a column vector v = [n; p; h], where n, p, and h represent the number of people in the population who are negative, positive, and hospitalised respectively, write down a matrix M for which [n', p', h'] = M[n; p; h], where [n', p', h'] represents the column vector of negative, positive, and hospitalised members of the population in the following week. (b) Show that M is diagonalisable over R and write down its three eigenvalues, ordered in such a way that 11 > d2 > 13. (You may use the computer to do this calculation if you prefer, e.g., by using the mateigen command in Pari-GP.) (c) Write down eigenvectors v1, v2, V3 attached to 11, â2 and 13 respectively.
aiShot(购买解锁去水印) The public health authorities of a small town have divided the population into three categories: covid- negative, covid-positive, and hospitalised. After performing regular, extensive tests, they have observed that in each successive week: • Among those who are negative, 95% remain so, 4% become positive, and 1% need to be hospitalised. • Among those who are positive, 75% recover and become negative, 20% stay positive, and 5% need to be hospitalised. • Among those who are hospitalised, 60% recover and become negative, 30% are released from hospital but remain positive, and 10% remain hospitalised. (a) After representing the population in a given week as a column vector v = [n; p; h], where n, p, and h represent the number of people in the population who are negative, positive, and hospitalised respectively, write down a matrix M for which [n', p', h'] = M[n; p; h], where [n', p', h'] represents the column vector of negative, positive, and hospitalised members of the population in the following week. (b) Show that M is diagonalisable over R and write down its three eigenvalues, ordered in such a way that 11 > d2 > 13. (You may use the computer to do this calculation if you prefer, e.g., by using the mateigen command in Pari-GP.) (c) Write down eigenvectors v1, v2, V3 attached to 11, â2 and 13 respectively.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 14PPS
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Question
![In this question, the real numbers in your answers should be given with three significant digits of accuracy
afiShot(购买解锁去水印)
The public health authorities of a small town have divided the population into three categories: covid-
negative, covid-positive, and hospitalised. After performing regular, extensive tests, they have observed
that in each successive week:
Among those who are negative, 95% remain so, 4% become positive, and 1% need to be
hospitalised.
• Among those who are positive, 75% recover and become negative, 20% stay positive, and 5% need
to be hospitalised.
• Among those who are hospitalised, 60% recover and become negative, 30% are released from
hospital but remain positive, and 10% remain hospitalised.
(a) After representing the population in a given week as a column vector v = [n; p; h], where n, p, and h
represent the number of people in the population who are negative, positive, and hospitalised
respectively, write down a matrix M for which [n', p', h'] = M[n; p; h], where [n', p', h'] represents
the column vector of negative, positive, and hospitalised members of the population in the following
week.
(b) Show that M is diagonalisable over R and write down its three eigenvalues, ordered in such a way
that 21 > 12 > 13. (You may use the computer to do this calculation if you prefer, e.g., by using the
mateigen command in Pari-GP.)
(c) Write down eigenvectors v1, v2, V3 attached to 11, 22 and 23 respectively.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc79b5872-5454-47e7-879f-2f12291cac41%2F665df4e4-0123-4cb1-a93e-686ddd23e19b%2Fxrhyjfm_processed.png&w=3840&q=75)
Transcribed Image Text:In this question, the real numbers in your answers should be given with three significant digits of accuracy
afiShot(购买解锁去水印)
The public health authorities of a small town have divided the population into three categories: covid-
negative, covid-positive, and hospitalised. After performing regular, extensive tests, they have observed
that in each successive week:
Among those who are negative, 95% remain so, 4% become positive, and 1% need to be
hospitalised.
• Among those who are positive, 75% recover and become negative, 20% stay positive, and 5% need
to be hospitalised.
• Among those who are hospitalised, 60% recover and become negative, 30% are released from
hospital but remain positive, and 10% remain hospitalised.
(a) After representing the population in a given week as a column vector v = [n; p; h], where n, p, and h
represent the number of people in the population who are negative, positive, and hospitalised
respectively, write down a matrix M for which [n', p', h'] = M[n; p; h], where [n', p', h'] represents
the column vector of negative, positive, and hospitalised members of the population in the following
week.
(b) Show that M is diagonalisable over R and write down its three eigenvalues, ordered in such a way
that 21 > 12 > 13. (You may use the computer to do this calculation if you prefer, e.g., by using the
mateigen command in Pari-GP.)
(c) Write down eigenvectors v1, v2, V3 attached to 11, 22 and 23 respectively.
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