How to get the correct result in a simple operation in Mathematica

Question

I have the following values for x[[i]], y[[i]] and A[[i,j]]:

x[[1]] = 4/5 x[[2]] = 31/39

y[[1]] = 2/5 y[[2]] = 145/357

A[[1,1]] = 62243/100000 A[[1,2]] = 3239/6250 A[[1,3]] = 17631/25000

I want to compute the value of an expression, specifically

A[[1, 3]] - A[[1, 1]]*x[[i]] - A[[1, 2]]*y[[i]]

So what I do is:

For[i = 1, i < 3, i++, error[[i]] = N[A[[1, 3]] - A[[1, 1]]*x[[i]] - A[[1, 2]]*y[[i]], 100]; ] error

So I get:

error[[1]] = 0 error[[2]] = -1.6871363930187...1687*10^-6.

But this is wrong since the correct result for the 1st loop is error[[1]] = -27/2500. The strange thing here is that if I compute (5*17361 - 62243 - 8*3239) / 125000 , which is practically the same operation, I get the correct result. What can I do to get the correct result? I used the N with precision of 100 digits, but obviously it is not working, FullForm neither.

Answer 1

The result from the loop is correct. You are using two different sets of numbers. Here is the loop computation without loops.

x = {4/5,31/39}
y = {2/5, 145/357}
A = {62243/100000, 3239/6250, 17631/25000}
A[[3]] - A[[1]]*x - A[[2]]*y  (* {0, -(261/154700000)} *)