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To RAJ: Define the determinant of...

To RAJ:

Define the determinant of a matrix a (written det(a)) recursively as follows:

1. if a is a 1 x 1 matrix, then det(a) = x

2. if a is of an order greater than 1, compute the determinant of a as follows:

a. Choose any row or column. For each element a[I, j] in this row or column, form the product:

power (-1, I + j) * a[I, j] * det(minor(a[I, j])

where I and j are the row and column positions of the element chosen, a[I, i] is the element chosen, det(minor(a[I, j]) is the determinant of the minor of a[I, j] and power (m, n) is the value of m raised to the nth power.

b. det(a) = sum of all these products.

Det(a) = Σ power(-1, I + j) * a[I, j] * det(minor(a[I, j]), for any j

or

Det(a) = Σ power(-1, I + j) * a[I, j] * det(minor(a[I, j]), for any i

As per the problem, write a program to compute the determinant of a matrix.

It should read a matrix, print it out, compute and print the determinant. Your program should be able to evaluate multiple matrices on a single execution. For class purposes your program should handle matrices up to and including those of order 6.

Use of recursion is okay but not mandatory. Use some form of linked list structure to store the matrix. You may use double, single, circular or multilinked lists with or without headers. Please give this careful consideration.

In justifying your choice of data structures please consider real world constraints.

Justify your choice of recursion or iteration. Be sure to compare your results to what you observed in the last project. As a minimum use the following 8 matrices to test your program. Use the same required input and the same input format as the last assignment.

[5]

2 3

5 9

3 -2 4

-1 5 2

-3 6 4

2 4 5 6

0 3 6 9

0 0 9 8

0 0 0 5

2 4 5 6

0 0 0 0

0 0 9 8

0 0 0 5

2 0 0 0

0 3 0 0

0 0 9 0

0 0 0 5

2 4 0 6

1 3 0 0

4 0 0 8

2 5 0 5

6 4 6 4 6 4

1 2 3 4 5 6

6 5 4 3 2 1

3 2 3 2 3 2

4 6 4 6 4 6

1 1 1 1 1 1

Define the determinant of a matrix a (written det(a)) recursively as follows:

1. if a is a 1 x 1 matrix, then det(a) = x

2. if a is of an order greater than 1, compute the determinant of a as follows:

a. Choose any row or column. For each element a[I, j] in this row or column, form the product:

power (-1, I + j) * a[I, j] * det(minor(a[I, j])

where I and j are the row and column positions of the element chosen, a[I, i] is the element chosen, det(minor(a[I, j]) is the determinant of the minor of a[I, j] and power (m, n) is the value of m raised to the nth power.

b. det(a) = sum of all these products.

Det(a) = Σ power(-1, I + j) * a[I, j] * det(minor(a[I, j]), for any j

or

Det(a) = Σ power(-1, I + j) * a[I, j] * det(minor(a[I, j]), for any i

As per the problem, write a program to compute the determinant of a matrix.

It should read a matrix, print it out, compute and print the determinant. Your program should be able to evaluate multiple matrices on a single execution. For class purposes your program should handle matrices up to and including those of order 6.

Use of recursion is okay but not mandatory. Use some form of linked list structure to store the matrix. You may use double, single, circular or multilinked lists with or without headers. Please give this careful consideration.

In justifying your choice of data structures please consider real world constraints.

Justify your choice of recursion or iteration. Be sure to compare your results to what you observed in the last project. As a minimum use the following 8 matrices to test your program. Use the same required input and the same input format as the last assignment.

[5]

2 3

5 9

3 -2 4

-1 5 2

-3 6 4

2 4 5 6

0 3 6 9

0 0 9 8

0 0 0 5

2 4 5 6

0 0 0 0

0 0 9 8

0 0 0 5

2 0 0 0

0 3 0 0

0 0 9 0

0 0 0 5

2 4 0 6

1 3 0 0

4 0 0 8

2 5 0 5

6 4 6 4 6 4

1 2 3 4 5 6

6 5 4 3 2 1

3 2 3 2 3 2

4 6 4 6 4 6

1 1 1 1 1 1

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