Question

For which value of k will the vector v1=(1, −2, k) in R

3

be a linear combination of

v2 = (3, 0, −2) and v2= (2, −1, 5)?

Answer 1

$$\vec v_1=a\vec v_2+b\vec v _3$$

$$3a+2b=1$$

$$0-b=-2$$

$$-2a+5b=k$$

$$a=-1, b=2, k=12$$

$k=12$