HELP me please with MATLAB it is in the course introdunction to mathematical modeling 
Exercise 1. Buckinggham Pi Method with matlab The aim of this exercise is to use a Matlab code to solve a dimensional analysis problem for a physical phenomena. Consider for this problem the variables, indexed from 1 to 4: Variable 1: [V] = =, for the speed. Variable 2: [d] = L, fot the Length. Variable 3: [p] =*, for the density. Variable 4: [n] = ; for the viscosity. Variable 5: [j] = =, for the frequency. We need to define the fundamental dimensions for this problem, and assign an index for each diension: Variable 5: [1] = 1, for the frequency. We need to define the fundamental dimensions for this problem, and assign an index for each diension: Dimension 1: L, Length. Dimension 2: T, Time. Dimension 3: M, Mass. Dimension 4: , Temperature. (Remark: we don't need the temperature for this problem, but the Matlab Code, is general and propose this dimension.) 1. In this first section, we use the Buckingham-Pi theorem, as usual, manually: (a) You have to determine first the dimension of each variable. (b) How much dimensionless groups we need for The dimensional analysis by the Buckingham Pi method. (c) Deduce the relation that relates 1,9, m and h. 2. In this second section, we suggest to use the Matlab Code for te Buckingham-Pi theorem. Execute the Matlab code and compare the obtained results with the results obtained in the first section. 3. In this third section, we suggest to analyse the Matlab Code. (a) Build the Matrix A defined as follows: Ajj the coefficient on the ith row and the jth column is equal to the power of jt fundamental dimension in the expression of the dimension of the ith variable. (Exemple: the 3rd variable is the density p. The first dimension is the length L. We have then: A1,3 = -3.) (b) The powers (a1, 61, C1, di, e) of the first dimensionless group II are stored as the coefficients of a vector X1 of R. The 4th coefficient di (resp. 5th coefficient ei) is dedicated to the power of n (resp. f). It follows that di = 1 and ei = 0. By the same way, II2 is represented by the vector X2 = (az, b2, C2, d2, C2), and we have that d2 = 0 and e2 = 1. Verify that in the linear system AX 1 = 0 5. Exercise 1. Buckinggham Pi Method with matlab The aim of this exercise is to use a Matlab code to solve a dimensional analysis problem for a physical phenomena. Consider for this problem the variables, indexed from 1 to 4: Variable 1: [V] = =, for the speed. Variable 2: [d] = L, fot the Length. Variable 3: [p] =*, for the density. Variable 4: [n] = ; for the viscosity. Variable 5: [j] = =, for the frequency. We need to define the fundamental dimensions for this problem, and assign an index for each diension: Variable 5: [1] = 1, for the frequency. We need to define the fundamental dimensions for this problem, and assign an index for each diension: Dimension 1: L, Length. Dimension 2: T, Time. Dimension 3: M, Mass. Dimension 4: , Temperature. (Remark: we don't need the temperature for this problem, but the Matlab Code, is general and propose this dimension.) 1. In this first section, we use the Buckingham-Pi theorem, as usual, manually: (a) You have to determine first the dimension of each variable. (b) How much dimensionless groups we need for The dimensional analysis by the Buckingham Pi method. (c) Deduce the relation that relates 1,9, m and h. 2. In this second section, we suggest to use the Matlab Code for te Buckingham-Pi theorem. Execute the Matlab code and compare the obtained results with the results obtained in the first section. 3. In this third section, we suggest to analyse the Matlab Code. (a) Build the Matrix A defined as follows: Ajj the coefficient on the ith row and the jth column is equal to the power of jt fundamental dimension in the expression of the dimension of the ith variable. (Exemple: the 3rd variable is the density p. The first dimension is the length L. We have then: A1,3 = -3.) (b) The powers (a1, 61, C1, di, e) of the first dimensionless group II are stored as the coefficients of a vector X1 of R. The 4th coefficient di (resp. 5th coefficient ei) is dedicated to the power of n (resp. f). It follows that di = 1 and ei = 0. By the same way, II2 is represented by the vector X2 = (az, b2, C2, d2, C2), and we have that d2 = 0 and e2 = 1. Verify that in the linear system AX 1 = 0 5
