ACTIVITY 2.10
MORE ABOUT LINEAR COMBINATIONS

In this activity, we will solve the reverse problem of the previous activity: express a vector like a combination linear of others two vectorsand. That is to say, find two scalar x and y that they verify = x+ y.

If we know the components of the three vectors, that is to say,

= (w ₁, w ₂),= (a ₁, a ₂) and= (b ₁, b ₂)

to expresslike a linear combination ofandWe will must solve the vector equation

(w ₁, w ₂) = x (a ₁, a ₂) + y (b ₁, b ₂)

This vector equation is equivalent to the following system of two equations with two unknown quantity

 x a ₁ + y b ₁ = w ₁
 x a ₂ + y b ₂ = w ₂

INTERACTIVE ACTIVITY

In this construction you have the vector expressed as a linear combination of and :

= x+ y

You express the following vectors like a linear combination of and . You solve the problem numerically and later you check the result using applet.

1) = (8,2)

2) = (-2,7)

3) = (-8, -5)

4) = (8,-4)

SOLUTION

END OF ACTIVITY 2.10
MORE ABOUT LINEAR COMBINATIONS