Finding linear combination between 3 vectors

Express(1,-2,5) in R^3 as linear combination of (1,1,1),(1,2,3),(2,-1,1)

[chicken vector]

What did you try?

[Torsten]

Hint:

Expressing (1,-2,5) as a linear combination of (1,1,1),(1,2,3),(2,-1,1) means solving the linear system

[[1,1,1].',[1,2,3].',[2,-1,1].']*x = [1,-2,5].'

Answer 1

[Sufiyan]

Hi,

You can refer to the below code to find linear combination between three vectors.

a=[1 1 1]';
b=[1 2 3]';
c=[2 -1 1]';
d=[1 -2 5]';
%unknown variables
syms k1 k2 k3
%equation
eqns = (k1.*a)+(k2.*b)+(k3.*c)-d==0 ;
vars = [k1 k2 k3];
[k1, k2, k3] = solve(eqns,vars)

k1 = 

k2 = 

3

k3 = 

2

Hope this helps!