What is the formula of left devision?

When I key in

a=[1 2 4];b=[2 4 7]; >> z=a'\b'

then i get this value z =

    1.8095

may i know what is the formula to get this value? Thanks.

Answer 1

[dpb]

doc mldivide  % and follow links therein

[Jing Lin Ng]

hi I do go through doc mldivide. but I do not know how to get the answer manually. I do not understand the formula behind this equation. do you know about this formula?

[dpb]

It's solution to a*z=b which is a least-squares problem formulation w/o an intercept. Matlab has a number of different ways to actually solve the system depending on the analyzed characteristics of a. These are discussed in the previous links. Seems like there's some more discussion in Cleve's Corner from the past. Possibly a search at mathworks.com could uncover a little more in depth but the actual algorithms are proprietary.

Try

a*z

from command line and see what you get.

Or,

regress(b',a')
ans =
  1.8095

if you have the Statistics Toolbox for another way to fit the model. Or, you should be able to write the least squares equations and solve analytically for this small a system.