Linear Algebra

Q6. f(x) = 2x² + ax²+bx+2, where a and b are constants. Given that x - 1 and x-2 are factors of f(x), find the value of a and the value of b.

Problem 7. Suppose the eigenvector matrix S has STS-¹. Show that A = SAS-¹ is symmetric and has orthogonal eigenvectors.

Problem 9. Suppose there is an epidemic in which every month half of those who are well become sick, and a quarter of those who are sick become dead. Find the steady state for the corresponding Markov process:

Problem 10. Write the 3 by 3 transition matrix for a controls course that is taught in two sections, if every week of those in Section A and of those in Section B drop the course, and of each section transfer to the other section.

Problem 12. (a) When do the the eigenvectors for 2 = 0 span the nullspace (A)? (b) When do all the eigenvectors for 20 span the column space C(A)?

Problem 15. Decide on the stability or instability of dv/dt =w,dw/dt = v. Is there a solution that decays?

227. Prove that a determinant remains unchanged if from each row (except the last one) we subtract all succeeding rows.

The mass, M, of ibuprofen in the bloodstream is given by the equation M=(0.69)', where I is the initial dose and t is the number of hours since the dose. Suppose a patient is given an initial dose of 200 mg. When will the amount of ibuprofen in the bloodstream be reduced by a factor of one-half? Round your answer to the nearest tenth of an hour. [5 marks]

Describe 3 situations of when or where rational numbers or integers are used in real life, using specific examples.

Write your own word problem that could be used to solve the following expression. Then, solve it: -20+32 %=