Observe the following system of nonlinear equations: 3.2 x3 4.1 x 1.1y + 8.2 = 0...

  

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Observe the following system of nonlinear equations: 3.2 x3 4.1 x 1.1y + 8.2 = 0 - - 19.4 x 1.2 y 30.3 = 0 - - (a) Use Matlab's plotting function to identify the number of intersections these two functions have. Namely, plot and identify by eye how many there are and roughly where they are - of course, please enclose the plots with your markings of where those intersections should be. For full credit, justify the domain of x-s for which you will do these plots that will give you the rough locations of all the roots! (5 pts) (b) Write a Matlab program (or programs) to find all intersections of these two curves. Hint: select an initial guess near each zero and start the procedure from that point. For your own records, keep tracking the progress of your iterations to make sure that you are converging to the correct intersection and then report iterations for the procedure that successfully converged to each of your intersections) (15 pts) Observe the following system of nonlinear equations: 3.2 x3 4.1 x 1.1y + 8.2 = 0 - - 19.4 x 1.2 y 30.3 = 0 - - (a) Use Matlab's plotting function to identify the number of intersections these two functions have. Namely, plot and identify by eye how many there are and roughly where they are - of course, please enclose the plots with your markings of where those intersections should be. For full credit, justify the domain of x-s for which you will do these plots that will give you the rough locations of all the roots! (5 pts) (b) Write a Matlab program (or programs) to find all intersections of these two curves. Hint: select an initial guess near each zero and start the procedure from that point. For your own records, keep tracking the progress of your iterations to make sure that you are converging to the correct intersection and then report iterations for the procedure that successfully converged to each of your intersections) (15 pts)