A question on linear algebra(also Matlab related)

[mech-eng]

Hi, Can someone explain me the division operation in the picture. First for left division we use (.\ ) not only ( \ ) And it is strange that when we divide first column of A by first column of B( here first column of B is 44) how can we find -5.1250 ?

 

[micromass]

The operation A\b solves the system $Ax = b$. So it is not division.

http://www.mathworks.nl/help/matlab/math/systems-of-linear-equations.html

 

[mech-eng]

The operation A\b solves the system $Ax = b$. So it is not division.

http://www.mathworks.nl/help/matlab/math/systems-of-linear-equations.html

But in the picture the writer says it is a left division and Matlab use it to solve systems.

 

[MarneMath]

That just happens to be what MATLAB calls the method that solves the linear system. A person could also write it as mldivide(A,b). Also, in MATLAB A.\B nd A\B are equivalent statements. Try it out.

 

[HallsofIvy]

That's NOT standard notation. If Ax= b (and A is invertible) then $x= A^{-1}b$. if xA= b then $x= bA^{-1}$. Because standard division (a/b) does not distinguish between "divide on the left" and "divide on the right" we don't normally use that notation.

That particular author (and possibly math lab- I don't use it) is using a special notation to distinguish between "division on the left" ($A^{-1}b$) and "division on the right" ($bA^{-1}$).