How to resolve the algorithm Cramer's rule step by step in the Racket programming language

Published on 12 May 2024 09:40 PM
#Racket

How to resolve the algorithm Cramer's rule step by step in the Racket programming language

Table of Contents

Problem Statement

Given

which in matrix format is

Then the values of

x , y

{\displaystyle x,y}

and

z

{\displaystyle z}

can be found as follows:

Given the following system of equations:

solve for

w

{\displaystyle w}

,

x

{\displaystyle x}

,

y

{\displaystyle y}

and

z

{\displaystyle z}

, using Cramer's rule.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Cramer's rule step by step in the Racket programming language

Source code in the racket programming language

#lang racket
(require math/matrix)

(define sys
  (matrix [[2 -1 5 1]
           [3 2 2 -6]
           [1 3 3 -1]
           [5 -2 -3 3]]))

(define soln
  (col-matrix [-3 -32 -47 49]))

(define (matrix-set-column M new-col idx)
  (matrix-augment (list-set (matrix-cols M) idx new-col)))

(define (cramers-rule M soln)
  (let ([denom (matrix-determinant M)]
        [nvars (matrix-num-cols M)])
    (letrec ([roots (λ (position)
                      (if (>= position nvars)
                          '()
                          (cons (/ (matrix-determinant
                                    (matrix-set-column M soln position))
                                   denom)
                                (roots (add1 position)))))])
      (map cons '(w x y z) (roots 0)))))

(cramers-rule sys soln)

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