Could you please help me out to get equations from augmented matrix

Questions
,
1

Hi,
I am trying to derive equations from an augmented matrix, but i’m not been able to, could anyone please help me out to convert these printed equations into real algebraic equations.
Regards.

Clear[a, b, c, d, e];
For[j = 1, j <= 5, j++,
 a = RandomInteger[{-5, 5}, {5, 6}];
 b = a[[1 ;; 5, 1 ;; 5]];
 c = Table[Subscript["x", i], {i, 1, 5}];
 d = b.c;
 e = 
\!\(\*SubscriptBox[\(a\), \(\(\[LeftDoubleBracket]\)\(All, 
   6\)\(\[RightDoubleBracket]\)\)]\);
 For[i = 1, i <= 5, i++,
   Print[
\!\(\*SubscriptBox[\(d\), \(\(\[LeftDoubleBracket]\)\(i\)\(\
\[RightDoubleBracket]\)\)]\), " = ", 
\!\(\*SubscriptBox[\(e\), \(\(\[LeftDoubleBracket]\)\(i\)\(\
\[RightDoubleBracket]\)\)]\)];]
  Print[" "];]

the notebook file is also attached.

2

Use Table to actually create and return a list rather than simply print it.

Table[
 a = RandomInteger[{-5, 5}, {5, 6}];
 b = a[[1 ;; 5, 1 ;; 5]];
 c = Array[x, 5];
 d = b.c;
 e = a[[All, 6]];
 Thread[d == e], {j, 5}]

(* Out[10]= {{5 x[1] - 2 x[2] - 3 x[3] - 4 x[4] - 4 x[5] == -2, 
  x[2] + 3 x[3] - 4 x[5] == -4, -2 x[1] + 5 x[2] - 4 x[3] - 3 x[5] == 
   1, 2 x[1] - 4 x[2] - 3 x[3] + 3 x[4] == -4, -3 x[1] - x[3] + 
    3 x[4] - 4 x[5] == 
   3}, {x[1] + 4 x[2] - 4 x[3] + 5 x[4] + 2 x[5] == 
   4, -5 x[1] + x[3] + 3 x[5] == 
   2, -x[1] - 2 x[2] + 5 x[3] - 3 x[4] + x[5] == -5, -2 x[1] + 
    4 x[2] - x[3] - 5 x[4] + 3 x[5] == -4, 
  5 x[1] + 2 x[2] - x[4] + 4 x[5] == 
   1}, {-x[1] - 4 x[2] + 3 x[3] + 2 x[4] - 4 x[5] == -4, -5 x[1] - 
    5 x[2] - 3 x[3] + x[4] - 3 x[5] == -3, -x[2] + 3 x[3] + 5 x[4] == 
   1, -4 x[1] - 3 x[3] - x[4] + 2 x[5] == -1, -5 x[1] + x[2] + 
    2 x[3] + 5 x[4] + x[5] == -5}, {x[1] + 5 x[2] + 2 x[3] - 4 x[4] ==
    3, 2 x[1] - 5 x[2] + 4 x[3] - 4 x[4] + 3 x[5] == -4, -3 x[1] + 
    x[2] - 4 x[3] - 4 x[4] - 4 x[5] == -5, 
  x[1] - 5 x[2] + x[3] - 3 x[4] - 2 x[5] == 0, 
  x[1] - x[2] - 2 x[4] - x[5] == 
   0}, {2 x[1] - 4 x[2] + 5 x[3] - 2 x[4] - x[5] == 
   1, -x[1] + 2 x[2] - 5 x[3] - 4 x[4] - x[5] == 
   2, -x[1] + x[2] - 3 x[3] - 3 x[5] == 5, 
  3 x[1] - 5 x[2] + 5 x[3] + x[4] - 5 x[5] == -5, -3 x[1] + x[2] + 
    2 x[3] + 5 x[4] - 3 x[5] == -3}} *)
3

I was curious to see if I could get Muzahoo jee’s subscripted form. Combining his and Daniel Lichtblau’s code, I came up with this:

Table[a = RandomInteger[{-5, 5}, {5, 6}];
 b = a[[1 ;; 5, 1 ;; 5]];
 c = Table[Subscript[x, i], {i, 1, 5}];
 d = b.c;
 e = a[[All, 6]];
 Thread[d == e], {j, 5}]

Hey, for me that’s a big deal!

Cheers,
Eric

4

That is a great help, Regards

5

that is really good
regards