Solve systems of linear equations Ax = B for x

x = A\B solves the system of linear equations A*x = B. The matrices A and B must have the same number of rows.

But ,what is the operation between the rows?

There is any one can solve this example–manually ?

A =

1 3

4 2

b= [6 ;7];

>> A\b

ans =

0.9000

1.7000

How to find 0.9 and 1.7 exactly?

Answer 1

[Stephen23]

"But ,what is the operation between the rows?"

Both mldivide and mrdivide can use many different algorithms for solving systems of linear equations, as documented in the mldivide documentation. There is no single "operation" that describes all of those algorithms.

"There is any one can solve this example–manually ?"

This is easy using standard definitions for solving linear equations, e.g. elimination of variables:

https://en.wikipedia.org/wiki/System_of_linear_equations#Elimination_of_variables

System definition:

First solve the first equation for x:

Second, substitute x back into the second equation:

Third, solve that for y:

And finally try them with your example values:

>> A = [1,3;4,2]
A =
     1     3
     4     2
>> b = [6;7]
b =
     6
     7
>> A\b
ans =
          0.9
          1.7
>> y = (A(1,1)*b(2)-A(2,1)*b(1)) ./ (A(1,1)*A(2,2)-A(2,1)*A(1,2))
y =
          1.7
>> x = (b(1)-A(1,2)*y) ./ A(1,1)
x =
          0.9

Answer 2

[KALYAN ACHARJYA]

ans =
    0.9000
    1.7000

How to find 0.9 and 1.7 exactly??

format shortg;
A =[1     3
    4     2];
b= [6 ;7];
A\b

Result:

ans =
          0.9
          1.7

Answer 3

[Torsten]

https://en.wikipedia.org/wiki/Cramer%27s_rule