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(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.

(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.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.3: The Gram-schmidt Process And The Qr Factorization
Problem 4BEXP
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In this question, the real numbers in your answers should be given with three significant digits of accuracy after the decimal point. 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.
Transcribed Image Text:In this question, the real numbers in your answers should be given with three significant digits of accuracy after the decimal point. 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.
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