Linear Algebra

Question 35 Solving Radical Equations Graphically Given the function f(x) = 3√√4 + 2x find x when f(x) = 18 using your graphing calculator. Then follow the steps below to show the intersection graph on the computer. [Hint: Use the following window on your graphing calculator: Xmin = -4, Xmax = 18, Ymin = -2, Ymax =20] 1. Write the point of intersection as an ordered pair below. Round the value of x to two decimal places as needed. If the point of intersection does not exist, enter DNE 18. 2. Use the Line Tool to draw the Horizontal Line y 3. Use the Square Root Tool to draw f(x) = 3√4 + 2x. To draw this function, first plot the point furthest to the left, followed by one more point. 4. Use the Point Tool to identify the point of intersection if it exists. 20+ 19 18 17 16 15 14 Wo A -4 -3 -2 -1 Point of Intersection: 13 12 11 10 9 8 N 7 s6 s6 5 4 3 S < 2 > 27 1 -1 -2 3√4 + 2x 2 3 4 Clear All Draw: = 18 8 9 10 11 12 13 14 15 16 17 18

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 13. write the general solution to du/dt = Au, and the specific solution that matches (0) =(3, 1). What is the steady state as f→00?

Problem 14. If P is a projection matrix, show from the infinite series that

Find the graph y = -sin(0+r/3) for 0<0<2r. Classify the function f(x)=6x3 - 2x2 as odd, even or neither.

Problem 16. In most applications the second-order equation looks like Mu" +Ku=0, with a mass matrix multiplying the second derivatives. Substitute the pure exponential u = ex and find the "generalized eigenvalue problem" that must be solved for the frequency and the vector .x.

Problem 17. From this general solution to du/dt = Au, find the matrix A:

Problem 18. A door is opened between rooms that hold v(0) = 30 people and w(0) = 10 people. The movement between rooms is proportional to the difference v-w: