please do questions d and e (d) Show that v1 can be normalised so the the sum of its coordinates is equal to 1, and, with thisnormalisation, show that, for any triple v = [n; p; h],v = Pv1 + av2 + bv3where P = n+ p + h is the total population, and a and b are some real numbers (which you do not needto bother calculating.)(e) Use the result of part (d) to show that, no matter what the initial state of the population, the proportionof people in the population who are negative, positive, and hospitalised will, over time, stabilise to fixedpercentages of the population. What are these percentages? In this question, the real numbers in your answers should be given with three significant digits of accuracyafter 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 observedthat 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 tobe hospitalised.Among those who are hospitalised, 60% recover and become negative, 30% are released fromhospital 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 hrepresent 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 columnvector of negative, positive, and hospitalised members of the population in the following week.

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The population has been divided into three categories: covid-negative, covid-positive, and…