Description
Given an N × N matrix A with entries aij , 1 ≤ i, j, ≤ N, the determinant can be found by the
following formula:
det(A) = ∑
N
j=1
(−1)j+1 × a1j × det(A1j ) (7.1)
where A1j is an (N − 1) × (N − 1) submatrix of A with row 1 and column j removed.
For example, given
A =
a11 a12 a13
a21 a22 a23
a31 a32 a33
(7.2)
then
det(A) = a11 × det(
[
a22 a23
a32 a33]
) − a12 × det(
[
a21 a23
a31 a33]
) + a13 × det(
[
a21 a22
a31 a32]
) (7.3)
= a11(a22a33 − a32a23) − a12(a21a33 − a31a23) + a13(a21a32 − a31a22) (7.4)
This is an example of recursive definition in mathematics. Using the recursive definition of determinant,
Eq. (7.1), please write a C program to
1. read in a matrix,
2. calculate it’s determinant using a recursive function, det. The declaration of det function is as
following.
double det(double A[N][N],int dim);
The det function returns the determinant of matrix A as a double precision number. And it has
two arguments, the two-dimensional N × N array A and an integer dim, that specifies the real size
of the matrix. Since the determinant is evaluated recursively, this dim may vary even though A can
stay as a fixed-size array. The constant N should be defined as a macro.
3. Once the determinant is obtained, your program prints the answer.
To test out your program, 12 matrices with various dimensions are also given. They are: mat1.in
– mat12.in. Since these matrices have different dimensions, your program needs to be recompiled with
different N to be able to solve different input matrices. To facilitate such recompilation, please use the
following C preprocessing directive to define N.
#if !defined(N)
#define N 3
#endif
If this is done, then we can recompile and execute your program without editing the file, as shown below.
$ gcc -DN=7 lab07.c
$ ./a.out < mat7.in
1
Note that the second command above executes the program a.out and read the file mat7.in as the
standard input. Thus, we don’t need to retype the matrix using keyboard.
Example of program execution is shown below.
$ gcc -DN=3 lab07.c
$ ./a.out < mat1.in
Matrix A is
1 2 3
4 5 6
7 8 9
det(A) = 0
Notes.
1. Create a directory lab07 and use it as the working directory.
2. Name your program source file as lab07.c.
3. The first few lines of your program should be comments as the following.
/* EE231002 Lab07. Matrix Determinant
ID, Name
Date:
*/
4. After finishing editing your source file, you can execute the following command to compile it,
$ gcc lab07.c
If no compilation errors, the executable file, a.out, should be generated, and you can execute it by
typing
$ ./a.out < mat1.in
5. Since the matrices provided have different dimensions, please open the file to find out its dimension,
then recompile with suitable N before solving for its determinant.
6. You can use unix time command to find the execution time of your program with different matrix
sizes. It is a good idea to find how the CPU time changes with matrix dimension.
$ time ./a.out < mat1.in
7. After you finish verifying your program, you can submit your source code by
$ ∼ee231002/bin/submit lab07 lab07.c
If you see a ”submitted successfully” message, then you are done. In case you want to check which
file and at what time you submitted your labs, you can type in the following command:
$ ∼ee231002/bin/subrec
It will show the last few submission records.
8. You should try to write the program as efficient as possible. The format of your program should be
compact and easy to understand. These are part of the grading criteria.
