Project 3: Matrix Operations

Project Objective:

1. user interface de sign and implementation
2. basic matrix operations
3. multi-dimensional array manipulation
4. function and recursion

Project Description:

In this project, you will design and implement a program to perform the basic matrix
operations: negation, transpose, addition, multiplication, and de terminant calculation . Your
program should 1) read in a list of matrices from an input file, 2) provide a user interface to ask
users to enter the matrix operation they want to perform, and 3) print out the result on the screen.
The executable of a master program and a sample input file will be provided as usual.

Basics on Matrix

A matrix is a rectangular (two-dimensional) array of elements (integers in this project),
each element is labeled by its row and column. For example, the following is a 2x3 matrix

2 5 8
1 3 6

It has two rows and three columns, which we refer to as the size (2x3) of the matrix. The
element 5 is said to be at coordinates (1,2), meaning that it is located at the intersection of the
first row and the second column.

A general matrix is denoted by A_nxm, where n and m are the numbers of rows and
columns in the matrix. a_ij(or a(i,j)) stands for the element in the i-th row and j-th column.

The negation of a matrix A_nxm is a matrix B_nxm of the same size where b_ij = -a_ij for all
1≤i≤n and 1≤j≤m. In other words, each element is negated. The negation of a matrix A is usually
denoted as –A.

The transpose of a matrix A_nxm is a matrix  B_mxn where b_ji = a_ji for all 1≤i≤n and 1≤j≤m.
In other words, the first row of matrix A_nxm becomes the first column of matrix B_mxn, the second
row of matrix A_nxm becomes the second column of matrix B_mxn, etc. Note that the size of B is
different from that of A because the order of n and m (i and j) has been switched. The transpose
of a matrix A is usually denoted as A^T (we use T(A) in this project).

For example, given the 2x3 matrix A defined above, we have

You can add two matrices of the same size. The sum will be a matrix of the same size as
the operand matrices, and is calculated by adding the matrices element by element. That is, A_nxm
+ B_nxm = C_nxm, where c_ij = b_ij + a_ij for all 1≤i≤n and 1≤j≤m.

Matrix multiplication can be d one between to matrices if the number of columns in the
first matrix equals the number of rows in the second matrix. The product will be a matrix that has
the same number of rows as the first matrix and the same number of columns as the second
matrix. That is, for all 1≤i≤n and
1≤j≤k. For example,

where, 93 = 2*2+5*5+8*8, 65 = 2*1+5*3+8*6, 65 = 1*2+3*5+6*8, and 46 = 1*1+3*3+6*6.
Note that A·B are B·A are generally different.

The determinant of a square matrix A_nxn (matrix that has the same number of rows and
columns) is denoted det (A_nxn) and can be calculated as follows:

where is an (n-1)x(n-1) matrix constructed by deleting the first row and the i-th column of
A_nxn. For example,

Input and Output

(1). Your program will read in a list of matrices from an input file. Each matrix starts with
one line that has a single character matrix name, an integer for the number of rows (n), and an
integer for the number of columns (m), followed by n lines of integers with m integers on each
line. A new matrix starts on the next line with the same format.

For example, the input for the above matrix A is:
A 2 3
2 5 8
1 3 6
For this project, the input file contains at most six (6) matrices and each matrix has no
more than ten (10) rows and no more than ten (10) columns.

(2). Your program will print out the following user interface that lists the above five matrix
ope rations and the option to quit:

Please select from the following matrix operations:
1. Negate matrix
2. Transpose matrix
3. Calculate determinant
4. Add matrices
5. Multiply matrices
6. Quit

Please select option:

(3). Following this prompt, the user will enter an option by its number (1 – 6), and your
program must check if the option entered is valid. If an invalid option is entered, not 1 – 6, you
must print the following error message on the next line

Invalid matrix operation.

and return to step (2).

(4). Based on the option that the user enters, your program will prompt the user to select
which matrix/matrices to use, by name. The first three operations are unary operations and will
prompt the user for 1 matrix, while the addition/multiplication operations are binary and will
prompt the user for 2 matrices. Your prompt must include the names of the matrices listed in the
input file. For example, if the input file contains three matrices named A, B, and C, then on the
following line, you should print out:

Select matrix (by name: A, B, C):

Note that for binary operations, this line will be printed twice.

If an invalid matrix name is entered (not among the names in the input file), then you will print
on the following line

Invalid matrix selection.

and proceed back to step (2). For binary operations, this message will be printed only once if
either matrix is incorrect, and after the prompt for the second matrix.

(5). After the program reads in the operation and valid matrix name(s), it will perform the
operation, print out the result, and go back to step (2). Not all operations will be possible for the
matrices selected. If an operation cannot be performed on the matrix/matrices selected, you will
print the appropriate error message (see below) and return to step (2).

When a valid option is entered along with valid matrix/matrices, you need to print out the result
starting from the next line and then return to step (2). If the result is an integer, print this integer.
If the result is a matrix, print the matrix out in the tabular format, with the columns aligned.

Note that none of these operations should change the original matrices. For example, when
negating a matrix, you print out the negated matrix, but the original matrix remains unchanged.

(6). When the user enters option 6, quit, you will print the following quit message and exit the
program. The quit message is:

Thanks for using the matrix operation program.

Project Requirements:

1. You must program using C under GLUE UNIX system and name your program p3.c.
2. Your program must be properly documented.
3. The determinant of a matrix must be calculated using a recursive function.
4. Submit your program p3.c electronically before the due time. Use the submit program to
do this. Also please do NOT send your input file.

IMPORTANT: Your program’s output should be exactly the same as that produced by the
master program. For your convenience, all the printf() statements used in the master program
are listed below:

// The option prompt:
printf("Please select from the following matrix operations:\n");
printf("\t1. Negate matrix\n");
printf("\t2. Transpose matrix\n");
printf("\t3. Calculate determinant\n");
printf("\t4. Add matrices\n");
printf("\t5. Multiply matrices\n");
printf("\t6. Quit\n");
printf("\nPlease select option: ");
printf("Thanks for using the matrix operation program.\n");
printf("Select matrix (by name: ");
// matrix selection prompt. use %c to print the matrix names
// separate different matrix names by comma and a space:“, “

// Error messages:
printf("Usage: executable input\n");
printf("ERROR: input file not found.\n");
printf("Invalid matrix selection.\n");
printf("Invalid matrix operation.\n");
printf("Cannot add these matrices.\n"); // if two matrices are of different size
printf("Cannot multiply these matrices.\n"); // if two matrices are of different size
printf("Cannot calculate the determinant of this matrix.\n"); // if the matrix is not a square matrix

// Print out formats:
printf("\n");
printf("%5d", a_ij); // aij is an element of the matrix, this is used to print out matrix
printf("\t%d\n", det); // use this format to print out the determinant of a square matrix

Grading Criteria:
 

These criteria will be strictly enforced and no exceptions will
be made. Make sure that the program that you submit is named
correctly (p3.c, with lower case p) and does compile.