The equation x=\vec(a) *(\vec(b) −\vec(c) ), where \vec(a) is a column vector

crazygbyo

crazygbyo

Answered question

2022-08-09

Say I have the equation
x = a ( b c )
where a is a column vector, b , and c are row vectors, x is a scalar, and a ( b c ) is taking the dot product between a and ( b c ). Is it possible to solve for b ?
I would naively think I could do this as
x = a ( b c )
x a T = | | a | | 2 ( b c )
x a T = | | a | | 2 b | | a | | 2 c
b = x a T + | | a | | 2 c | | a | | 2
But this does not seem correct when putting in concrete values. What am I doing wrong?

Answer & Explanation

nedervdq3

nedervdq3

Beginner2022-08-10Added 13 answers

If x , a , and c are all given then we can rearrange to get
b a = x + c a .
This is the equation of a hyperplane in R n (assuming that this is where your vectors live). In particular the solution is not unique unless n=1.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?