Hello Vedicmaths(a) If the first vector can be expressed as a linear combination of the other two, then you'll be able to find values of and for which

Comparing coefficients of , and :

(1)

(2)

(3)

So you've now got three equations in 2 unknowns. Use 2 of them to find values of and . Then plug these values into the third. If it works then, yes, you can do it; if it doesn't, you can't.

So in this case:

From (3):

Subst into (2):

And test in (1): , which is correct.

So, in this case, yes the first vector can be expressed as a linear combination of the other two. It is:

Use the same method in part (b).

Grandad