ACTIVITY 2.9
PRODUCTS BY SCALAR AND LINEAR COMBINATIONS

The product of a scalar m by a vector= (u _1, u₂) also is very easy to do when we work with components: each component multiplies ofby m

So, in the figure, you have made the two products:

 2= 2 (-3, 1) = (2 (-3,) 2 · 1) = (-6, 2)
= (4, 2) = ( 4, 2) = (-2, -1)

And the linear combination of the vectors= (u _1,u ₂) and= (v _1,v ₂)  built with the scalars m and n is the vector respectively

= m+ n= m(u₁,u₂)+n(v₁,v₂) = ( mu₁,mu₂)+(nv₁,nv₂) = (mu₁+nv₁,mu₂+nv₂)

In the bottom part of figure you have the linear combination

= 2= (-6,2) + (2, ) = (-4, 3)

INTERACTIVE ACTIVITY

Moving the green points you draw the following vectors fixing you in his components:

1) = 4 + 3

2) = 4 -

3) = -3 +

4) = -2 - 3

5) = 1,8 + 1,75

6) = -4 - 1,5

7) = 4,5

8) = -3

SOLUTION

They give you the vectors

END OF ACTIVITY 2.9
PRODUCTS BY SCALAR AND LINEAR COMBINATIONS