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Determinant of a Matrix

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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) =? power(-1, I + j) * a[I, j] * det(minor(a[I, j]), for any j;or;Det(a) =? power(-1, I + j) * a[I, j] * det(minor(a[I, j]), for any i;Write a Java program that reads a, print a in matrix form, and prints the value of det(a), where det is a method that computes the determinant of a matrix.;As per the problem, write a program that uses a recursive algorithm 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. Your program should handle matrices up to and including those of order 6. You are required to use an array for this problem. Your solution must be recursive.;Justify your data structures. Consider an iterative implementation. Would it be more efficient? What data structures would you choose in that case?;As a minimum, use the following eight matrices to test your program, formatted as shown to the right.;[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;SAMPLE INPUT;1;5;2;2 3;5 9;3;3 -2 4;-1 5 2;-3 6 4;Etc.

 

Paper#35233 | Written in 18-Jul-2015

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