1)
>> A = [1, 1, 1; 1, -1, 2; 1, -1, -3]

A =

     1     1     1
     1    -1     2
     1    -1    -3

>> b = [6; 5; -10]

b =

     6
     5
   -10

>> Ab = [A, b]

Ab =

     1     1     1     6
     1    -1     2     5
     1    -1    -3   -10

>> C = rref(Ab)

C =

     1     0     0     1
     0     1     0     2
     0     0     1     3

>> x = C(:, end)

x =

     1
     2
     3
>> x = inv(A) * b

x =

    1.0000
    2.0000
    3.0000

>> x = A\b

x =

     1
     2
     3
=====================================
2)
>> A = [1,1,1;2,-1,1;1,2,-1]

A =

     1     1     1
     2    -1     1
     1     2    -1

>> b = [12;7;6]

b =

    12
     7
     6

>> Ab = [A, b]

Ab =

     1     1     1    12
     2    -1     1     7
     1     2    -1     6

>> C = rref(Ab)

C =

     1     0     0     3
     0     1     0     4
     0     0     1     5

>> x = C(:, end)

x =

     3
     4
     5

>> x = inv(A) * b

x =

    3.0000
    4.0000
    5.0000

>> x = A\b

x =

    3.0000
    4.0000
    5.0000
=====================================
3)
>> A = [1, -1,1;1,1,1;2,2,-1]

A =

     1    -1     1
     1     1     1
     2     2    -1

>> b = [2;4;-4]

b =

     2
     4
    -4

>> Ab = [A, b]

Ab =

     1    -1     1     2
     1     1     1     4
     2     2    -1    -4

>> C = rref(Ab)

C =

     1     0     0    -1
     0     1     0     1
     0     0     1     4

>> x = C(:, end)

x =

    -1
     1
     4

>> x = inv(A)*b

x =

   -1.0000
    1.0000
    4.0000

>> x = A\b

x =

    -1
     1
     4
=====================================
4)
>> A = [2,1,-1;1,-3,-2;3,-2,-1]

A =

     2     1    -1
     1    -3    -2
     3    -2    -1

>> b = [-1;-12;-5]

b =

    -1
   -12
    -5

>> Ab = [A, b]

Ab =

     2     1    -1    -1
     1    -3    -2   -12
     3    -2    -1    -5

>> C = rref(Ab)

C =

    1.0000         0         0    0.7143
         0    1.0000         0    1.5714
         0         0    1.0000    4.0000

>> x = C(:, end)

x =

    0.7143
    1.5714
    4.0000

>> x = inv(A) * b

x =

    0.7143
    1.5714
    4.0000

>> x = A\b

x =

    0.7143
    1.5714
    4.0000
=====================================
5)
>> A = [2,3,1;6,-2,-1;3,1,-1]

A =

     2     3     1
     6    -2    -1
     3     1    -1

>> b = [1;-14;1]

b =

     1
   -14
     1

>> Ab = [A, b]

Ab =

     2     3     1     1
     6    -2    -1   -14
     3     1    -1     1

>> C = rref(Ab)

C =

     1     0     0    -2
     0     1     0     3
     0     0     1    -4

>> x = C(:, end)

x =

    -2
     3
    -4

>> x = inv(A) * b

x =

   -2.0000
    3.0000
   -4.0000

>> x = A\b

x =

    -2
     3
    -4
=====================================
6)
>> A = [5,-2,1;2,5,-2;1,-4,3]

A =

     5    -2     1
     2     5    -2
     1    -4     3

>> b = [24;-14;26]

b =

    24
   -14
    26

>> Ab = [A, b]

Ab =

     5    -2     1    24
     2     5    -2   -14
     1    -4     3    26

>> C = rref(Ab)

C =

     1     0     0     3
     0     1     0    -2
     0     0     1     5

>> x = C(:, end)

x =

     3
    -2
     5

>> x = inv(A) * b

x =

    3.0000
   -2.0000
    5.0000

>> x = A\b

x =

    3.0000
   -2.0000
    5.0000
=====================================
7)
>> A= [4,2,3;3,4,2;2,-1,5]

A =

     4     2     3
     3     4     2
     2    -1     5

>> b = [8;-1;3]

b =

     8
    -1
     3

>> Ab = [A, b]

Ab =

     4     2     3     8
     3     4     2    -1
     2    -1     5     3

>> C = rref(Ab)

C =

     1     0     0     5
     0     1     0    -3
     0     0     1    -2

>> x = C(:, end)

x =

     5
    -3
    -2

>> x = inv(A)*b

x =

     5
    -3
    -2

>> x = A\b

x =

    5.0000
   -3.0000
   -2.0000
=====================================
8)
>> A = [6,3,2;9,-1,4;10,5,3]

A =

     6     3     2
     9    -1     4
    10     5     3

>> b = [12;37;21]

b =

    12
    37
    21

>> Ab = [A, b]

Ab =

     6     3     2    12
     9    -1     4    37
    10     5     3    21

>> C = rref(Ab)

C =

     1     0     0     5
     0     1     0    -4
     0     0     1    -3

>> x = C(:, end)

x =

     5
    -4
    -3

>> x = inv(A)*b

x =

    5.0000
   -4.0000
   -3.0000

>> x = A\b

x =

    5.0000
   -4.0000
   -3.0000
=====================================
9)
>> A = [2,4,3;10,-8,-9;4,4,-3]

A =

     2     4     3
    10    -8    -9
     4     4    -3

>> b = [3;0;2]

b =

     3
     0
     2

>> Ab = [A, b]

Ab =

     2     4     3     3
    10    -8    -9     0
     4     4    -3     2

>> C = rref(Ab)

C =

    1.0000         0         0    0.5000
         0    1.0000         0    0.2500
         0         0    1.0000    0.3333

>> x = C(:, end)

x =

    0.5000
    0.2500
    0.3333

>> x = inv(A)*b

x =

    0.5000
    0.2500
    0.3333

>> x = A\b

x =

    0.5000
    0.2500
    0.3333
=====================================
10)
>> A = [3,1,1;1,2,-1;1,1,2]

A =

     3     1     1
     1     2    -1
     1     1     2

>> b = [1;1;-17]

b =

     1
     1
   -17

>> Ab = [A, b]

Ab =

     3     1     1     1
     1     2    -1     1
     1     1     2   -17

>> C = rref(Ab)

C =

     1     0     0     5
     0     1     0    -6
     0     0     1    -8

>> x = C(:, end)

x =

     5
    -6
    -8

>> x = inv(A)*b

x =

    5.0000
   -6.0000
   -8.0000

>> x = A\b

x =

    5.0000
   -6.0000
   -8.0000
=====================================
11)
>> A = [7,3,-4;3,-2,5;1,1,-6]

A =

     7     3    -4
     3    -2     5
     1     1    -6

>> b = [-35;38;-27]

b =

   -35
    38
   -27

>> Ab = [A, b]

Ab =

     7     3    -4   -35
     3    -2     5    38
     1     1    -6   -27

>> C = rref(Ab)

C =

     1     0     0     1
     0     1     0   -10
     0     0     1     3

>> x = C(:,end)

x =

     1
   -10
     3

>> x = inv(A)*b

x =

    1.0000
  -10.0000
    3.0000

>> x = A\b

x =

     1
   -10
     3
=====================================
12)
>> A = [4,-1,5;3,3,-4;6,2,-3]

A =

     4    -1     5
     3     3    -4
     6     2    -3

>> b = [-6;30;33]

b =

    -6
    30
    33

>> Ab = [A, b]

Ab =

     4    -1     5    -6
     3     3    -4    30
     6     2    -3    33

>> C = rref(Ab)

C =

     1     0     0     3
     0     1     0     3
     0     0     1    -3

>> x = C(:, end)

x =

     3
     3
    -3

>> x = inv(A)*b

x =

    3.0000
    3.0000
   -3.0000

>> x = A\b

x =

    3.0000
    3.0000
   -3.0000
=====================================
13)
>> A = [9,4,-10;6,-8,5;12,12,-15]

A =

     9     4   -10
     6    -8     5
    12    12   -15

>> b = [6;-1;10]

b =

     6
    -1
    10

>> Ab = [A, b]

Ab =

     9     4   -10     6
     6    -8     5    -1
    12    12   -15    10

>> C = rref(Ab)

C =

    1.0000         0         0    0.3333
         0    1.0000         0    0.2500
         0         0    1.0000   -0.2000

>> x = C(:,end)

x =

    0.3333
    0.2500
   -0.2000

>> x = inv(A)*b

x =

    0.3333
    0.2500
   -0.2000

>> x = A\b

x =

    0.3333
    0.2500
   -0.2000
=====================================
14)
>> A = [5,3,-1;10,-1,1;15,2,-1]

A =

     5     3    -1
    10    -1     1
    15     2    -1

>> b = [-11;10;-7]

b =

   -11
    10
    -7

>> Ab = [A, b]

Ab =

     5     3    -1   -11
    10    -1     1    10
    15     2    -1    -7

>> C = rref(Ab)

C =

    1.0000         0         0    0.2000
         0    1.0000         0   -2.0000
         0         0    1.0000    6.0000

>> x = C(:, end)

x =

    0.2000
   -2.0000
    6.0000

>> x = inv(A)*b

x =

    0.2000
   -2.0000
    6.0000

>> x = A\b

x =

    0.2000
   -2.0000
    6.0000
=====================================
15)
>> A = [1,1,0;0,1,1;1,0,1]

A =

     1     1     0
     0     1     1
     1     0     1

>> b = [1;-1;-6]

b =

     1
    -1
    -6

>> Ab = [A, b]

Ab =

     1     1     0     1
     0     1     1    -1
     1     0     1    -6

>> C = rref(Ab)

C =

     1     0     0    -2
     0     1     0     3
     0     0     1    -4

>> x = C(:, end)

x =

    -2
     3
    -4

>> x = inv(A)*b

x =

    -2
     3
    -4

>> x = A\b

x =

    -2
     3
    -4
=====================================
16)
>> A = [1,2,0;0,2,1;1,0,2]

A =

     1     2     0
     0     2     1
     1     0     2

>> b = [-1;0;11]

b =

    -1
     0
    11

>> Ab = [A, b]

Ab =

     1     2     0    -1
     0     2     1     0
     1     0     2    11

>> C = rref(Ab)

C =

     1     0     0     3
     0     1     0    -2
     0     0     1     4

>> x = C(:, end)

x =

     3
    -2
     4

>> x = inv(A)*b

x =

    3.0000
   -2.0000
    4.0000

>> x = A\b

x =

     3
    -2
     4
=====================================
17)
>> A = [0,1,1;2,0,1;2,3,0]

A =

     0     1     1
     2     0     1
     2     3     0

>> b = [-8;9;-3]

b =

    -8
     9
    -3

>> Ab = [A, b]

Ab =

     0     1     1    -8
     2     0     1     9
     2     3     0    -3

>> C = rref(Ab)

C =

     1     0     0     6
     0     1     0    -5
     0     0     1    -3

>> x = C(:, end)

x =

     6
    -5
    -3

>> x = inv(A)*b

x =

     6
    -5
    -3

>> x = A\b

x =

     6
    -5
    -3
=====================================
18)
>> A = [3,-2,0;0,3,-4;-5,0,1]

A =

     3    -2     0
     0     3    -4
    -5     0     1

>> b = [0;25;-14]

b =

     0
    25
   -14

>> Ab = [A, b]

Ab =

     3    -2     0     0
     0     3    -4    25
    -5     0     1   -14

>> C = rref(Ab)

C =

     1     0     0     2
     0     1     0     3
     0     0     1    -4

>> x = C(:, end)

x =

     2
     3
    -4

>> x = inv(A)*b

x =

    2.0000
    3.0000
   -4.0000

>> x = A\b

x =

    2.0000
    3.0000
   -4.0000
=====================================
19)
>> A = [-5,0,3;5,-3,0;0,3,-5]

A =

    -5     0     3
     5    -3     0
     0     3    -5

>> b = [10;-7;-13]

b =

    10
    -7
   -13

>> Ab = [A, b]

Ab =

    -5     0     3    10
     5    -3     0    -7
     0     3    -5   -13

>> C = rref(Ab)

C =

     1     0     0     1
     0     1     0     4
     0     0     1     5

>> x = C(:, end)

x =

     1
     4
     5

>> x = inv(A)*b

x =

    1.0000
    4.0000
    5.0000

>> x = A\b

x =

     1
     4
     5
=====================================
20)
>> A = [1,-2,0;0,1,-2;1,1,1]

A =

     1    -2     0
     0     1    -2
     1     1     1

>> b = [0;5;8]

b =

     0
     5
     8

>> Ab = [A, b]

Ab =

     1    -2     0     0
     0     1    -2     5
     1     1     1     8

>> C = rref(Ab)

C =

     1     0     0     6
     0     1     0     3
     0     0     1    -1

>> x = C(:, end)

x =

     6
     3
    -1

>> x = inv(A)*b

x =

     6
     3
    -1

>> x = A\b

x =

     6
     3
    -1
=====================================
21)
>> A = [5,0,-3;0,-1,2;1,2,-4]

A =

     5     0    -3
     0    -1     2
     1     2    -4

>> b = [2;-5;8]

b =

     2
    -5
     8

>> Ab = [A, b]

Ab =

     5     0    -3     2
     0    -1     2    -5
     1     2    -4     8

>> C = rref(Ab)

C =

     1     0     0    -2
     0     1     0    -3
     0     0     1    -4

>> x = C(:, end)

x =

    -2
    -3
    -4

>> x = inv(A)*b

x =

    -2
    -3
    -4

>> x = A\b

x =

    -2
    -3
    -4
=====================================
22)
>> A = [2,0,-1;4,1,-1;3,-1,5]

A =

     2     0    -1
     4     1    -1
     3    -1     5

>> b = [14;41;53]

b =

    14
    41
    53

>> Ab = [A, b]

Ab =

     2     0    -1    14
     4     1    -1    41
     3    -1     5    53

>> C = rref(Ab)

C =

     1     0     0    10
     0     1     0     7
     0     0     1     6

>> x = C(:, end)

x =

    10
     7
     6

>> x = inv(A)*b

x =

   10.0000
    7.0000
    6.0000

>> x = A\b

x =

    10
     7
     6
=====================================
23)
>> A = [1,1,-1;1,-1,1;-1,1,1]

A =

     1     1    -1
     1    -1     1
    -1     1     1

>> b = [1;3;7]

b =

     1
     3
     7

>> C = rref(Ab)

C =

     1     0     0     2
     0     1     0     4
     0     0     1     5

>> x = C(:, end)

x =

     2
     4
     5

>> x = inv(A)*b

x =

     2
     4
     5

>> x = A\b

x =

     2
     4
     5