Assignment Set - 8

Please write your Roll Number, Name and Assignment Number at the header of each program.

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Assignment 8.a:        Filename: a8a.c

You have to write a program that performs the following tasks:

1. It reads the value of integer N, and then reads in a two matrices of floats, namely A[N][N] and X[N].

2. It prints a saddle point of the matrix (if it exists). It must print both the value and the position of the saddle point.

3. Write a function to compute the product of matrices and use it to compute the product of the matrices A and X

4. It uses the upper triangulation approach to solve the set of linear equations specified by A and X. It must print the upper triangular matrix derived from A

Information:

• A saddle point is an element of the matrix which is both the smallest element in its row and the largest element in its column.
   

• For part 4, first construct an augmented matrix and then find the upper triangular matrix, as shown in the following example.

      2x + y - z   = 8
    -3x - y + 2z = -11
    -2x + y + 2z = -3

The augmented matrix is:

2	1	-1	8
-3	-1	2	-11
-2	1	2	-3

The upper triangular form is:

2	1	-1	8
0	1/2	1/2	1
0	0	-1	1

The values of x, y and z can now be computed by back substitution. The third row yields the value of z as -1. We can substitute this value and compute the value of y from the second row, and so on. In this example the values are: x=2, y=3, z= -1

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