how row 10 is Working Specific "A(i,k+1:n) " ??

Question

Raya Arafat 2020-10-26

回答： Rohit Pappu 2020-10-29

function [x,det] = gauss(A,b)

% Solves A*x = b by Gauss elimination and computes det(A).

% USAGE: [x,det] = gauss(A,b)

if size(b,2) > 1; b = b’; end % b must be column vector

n = length(b);

for k = 1:n-1 % elimination phase

for i= k+1:n

if A(i,k) ∼=0

lambda = A(i,k)/A(k,k);

A(i,k+1:n) = A(i,k+1:n) - lambda*A(k,k+1:n);

b(i)= b(i) - lambda*b(k);

end

if nargout == 2; det = prod(diag(A)); end

for k = n:-1:1 % back substitution phase

b(k) = (b(k) - A(k,k+1:n)*b(k+1:n))/A(k,k);

end; x = b;

Answer 1

Rohit Pappu 2020-10-29

Line no. 10 states that Update the (i)th row, (k+1)th to (n)th columns of A as follows

Multiply Lambda with the elements present in (k)th row, (k+1)th to (n)th columns of A to obtain a vector of dimensions (1, n-k)
Subtract the above resultant vector from the elements present in (i)th row, (k+1)th to (n)th columns of A to obtain a vector of dimensions (1, n-k)
Save the above resultant vector in (i)th row, (k+1)th to (n)th columns of A