Lab Activity 4 - Answers

Each question worth 2/5 points except #1 and #2 which are worth 6/5 points.

Part 1: Programming the function 'find_xy' .

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2. Write down the equation that you are going to solve, in the matrix form [matrix]*[column vector] = [column vector]. (Hint: see the matrix equation in the MP 1 write-up
immediately above equation_1.)
 

The following answers should also be typed, in sequence, in your find_xy.m file.

4. Fill in the blanks to create the matrix A_main. Assume that the variable N has already been created.

A_main  = diag(  -(K(1:N)+K(2:N+1)) , 0 ) ;
 
 

5. Fill in the blanks to create the matrix A_upper. Assume that the variable N has already been created.

A_upper  = diag(  K(2:N) , 1 ) ;
 
 

6. Fill in the blanks to create the matrix A_lower. Assume that the variable N has already been created.

A_lower  = diag(  K(2:N) , -1 ) ;
 

Now add the line of Matlab code,

A = A_main + A_upper + A_lower;

7. Fill in the blanks to modify the first and the last elements of the vector W :

W(1) = W(1) - K(1)*HL;

W(N) = W(N) - K(N+1)*HR ;
 
 

8. Fill in the blank to solve the system of equations using the backslash (\) operator, and store this result in a vector h.
 

 h = A \ W ;

9.  Fill in the blank to change h from a column vector into a row vector.

h = h' ;

10. Fill in the blank to prepend h with HL and append h with HR. (Hint: example, if h = [1 2 3 4 5] and HL = 0 , HR = 6 then we need to create [ 0 1 2 3 4 5 6])

h =  [HL  h  HR] or [HL, h, HR] ;

y = h;

11. Fill in the blank to create a row vector x of distances from the left tower. You should have N+2 (7 for our example) elements in this vector. Assume the variable d (with N+1 elements) has already been created. (Hint: use 'cumsum' and prepend 0 )

x = [0 cumsum(d)] ;