(2) Consider the system of linear differential equations: For this system: 2 $2 0 3 x2 (a) Compute the solution explicitly, showing the fundamental matrix of solutions. (b) Draw the phase portrait by solving (c) Calculate the orbits. dx2 3x2 dx1 2x1

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Write equations 3x – 4y = 7 and 2x + y = 1 as the matrix equation a () - () and then: Calculate the inverse matrix A-1.

You learnt from chemistry and ECH 3023 that hydrogen sulfide may be reacted with sulfur dioxide in a sulfur recovery raector in accordance with the equation: a H2 S + b SO2 → c S + d H2O Find the smallest positive integer values of the stoichiometric coefficients a, b, c and d by setting up a set of linear system of equations from the atomic balances and solving the linear system using Gauss elimination and back substitution. Show the details of your work.

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Q.2) Use Inverse matrix method to solve the following equations: *- y +z=1 2x – 2y + 2: = 2 -3x + 3y + 32 = -3

Exercises 1-6 refer to the folkowing systems of equations: (i) dx dt (i) dx 10x (1 – ) – 20xy ху 0.3x = dt 100 dy := 15y (1 -) + 25xy. dt 1. In one of these systems, the prey are very large animals and the predators are very small animals, such as elephants and mosquitoes. Thus it takes many predators to eat one prey, but each prey eaten is a tremendous benefit for the predator population. The other system has very large predators and very small prey. Determine which system is which and provide a justification for your answer

-[XX]-[2-3] + [2x] Solve for x, y, z, and win the matrix equation (x, y, z, W).

Solve the following equations system 0.1V, – j0.2V, =1 - j0.2V, +(0.2+ j0.3)V, = j0.5 ans V= 3.3333 + 3.3333i V, =1.6667 + 3.3333i

Find two linearly independent solutions of y" + 9xy = 0 of the form y₁=1+a3x³ +a6zº +... 32= x+bx+b7x² + ... Enter the first few coefficients: a3 a6 ba b7 || help (numbers) help (numbers) help (numbers) help (numbers)