Question

) Write the vector  = (, , ) as a linear combination of
 =(,,),  =(,,) =(,,),ifpossible

Answer 1

Here is an example of a solution:

v=<2,5,3>; u₁=<1,1,0>; u₂=<0,1,1>; u₃=<1,0,1>.

Let v=au₁+bu₂+cu₃, where a, b and c are scalars. We can write the following system of equations:

a+c=2

a+b=5

b+c=3

Add the first two equations together: 2a+b+c=7, 2a+3=7 (because b+c=3), a=2⇒c=0, b=3.

v=2u₁+3u₂, a unique solution.