Left Matrix Division

Left Matrix Division (A\B) is defined as solving the solution Ax = B.

Depending on whether A is square, under determined, or over determined, the way to solve this solution is different. When A is square, x = inv(A)*b is used to solve the solution. If A is over determined, the least squares solution is produced. If A is under determined, then a least squares solution with the maximum number of zeros is produced.

\ Scalar Row Vector Column Vector Matrix
Scalar Divides the second scalar by the first scalar. x = A\B solves Ax = B using left matrix division. x = A\B solves Ax = B using left matrix division. x = A\B solves Ax = B using left matrix division.
Row Vector x = A\B solves Ax = B using left matrix division. x = A\B solves Ax = B using left matrix division.    
Column Vector     x = A\B solves Ax = B using left matrix division. x = A\B solves Ax = B using left matrix division.
Matrix     x = A\B solves Ax = B using left matrix division. x = A\B solves Ax = B using left matrix division.

Examples

4 \ 6
ans = 1.5

[5 4 3]\[4 6 3]
ans =[0.4 0.6 0.3; 0.32 0.48 0.24; 0.24 0.36 0.18]

[4 2 9; 3 7 4] \ [6; 8]
ans = [Matrix] 3 x 1
0.30303
0.81212
0.35152

Invalid Examples

[4 2 9; 3 7 4] \ [9 3]
[5 8 3]\[8; 6; 2]