1.

Create a file containing a vector w and its length in the first line. The file should look in the following way:

N
w1
w2
w3
...
wN

2.

Write a program which contains a static array w of length MAX_N and three two-dimensional static arrays A, B and C of sizes \([MAX_N x MAX_M]\), \([MAX_M x MAX_L]\) and \([MAX_N x MAX_L]\) correspondingly.

3.

Read the length \(N\) of the vector w and and check if MAX_N\(\ge\)N. If the condition is fulfilled, read the vector into the array.

4.

Check if MAX_M\(\ge\)N and if the condition is satisfied, create the array B which elements are defined by the formula: \[ b_{ij} = \left\{ \begin{array}{ll} 1-w_i w_j,& \; i=j \\ -2w_i w_j,& \; i \ne j \end{array} \right. \] ## 5. Write a function which prints an array passed as its argument to the file “mac.txt”. Run the function with the array B as the argument.

6.

Write two functions:

1. the first one should compute a product of two matrices A and B: \(C = A \cdot B\), or in another way \(C_{ij} = \sum_{k=1}^M A_{ik} B_{kj}\)
2. the second one should compute a transposition of a given matrix.

7.

Use both functions from the point 6 and calculate the matrix: \(C = B \cdot B^T\).