How does Matlab divide two row vectors by each other to get a scalar?

Let's consider, A is a vector like shown:

A = [20 30 40];

and B is also a vector:

B = [5 10 20];

when you want to execute this operation:

C = B/A;

then you will get a scalar: 0.4137

if you want to check this answer by doing this:

C.*A

It should be got B again but you will get this vector instead:

ans =

8.2759 12.4138 16.5517

Could somebody explain what's going on?

[darova]

What about point (./) ?

[Adam]

doc mrdivide

explains that B/A is solving a set of linear equations x*A = B for x.

Clearly you can't expect to multiply A by any scalar and get B as the result. That is trivially obvious!

[Stephen23]

"It should be got B again"

Can you show us the system of equations for which this statement is true?

[Osama Tabbakh]

I was just an example for understanding how calculate matlab this scalar 0.4137 and why it is scalar.

Answer 1

[Star Strider]

To expand slightly on that, ‘C’ is the least-squares estimate of the slope of with the y-intercept forced through the origin:

figure
plot(A,B,'p',  A,C*A,'-r',  [0 A(1)],C*[0 A(1)],':k')
axis([0  45    0  25])

[Osama Tabbakh]

Thanks, could you please tell me how it can be solved manually by least-squares estimate (which equation is used for this).

[Star Strider]

As always, my pleasure.

Calculating the slope alone is straightforward (β is the slope parameter):

Set this equal to zero and solve to get:

If you want a more general solution, see the Wikipedia article on Linear least squares.

[Osama Tabbakh]

Thanks!

[Star Strider]

As always, my pleasure!

[Timo Tommila]

awesome, thank you I was wondering the same thing.

[Star Strider]

My pleasure!