10. determine whether or not, vectors ui(1,-2, 0, 3), u2 = (2, 3,0,-1), u3 = (3,9,-4,-2) e r is a linear combination of the (2,-1,2,1) 2

If (2, -1, 2, 1) is a linear combination of the three given vectors, then there should exist such that

or equivalently, there should exist a solution to the system

Right away we get , so the system reduces to

Notice that the first equation is the sum of the latter two. The third equation gives us

so that in the second equation,

which in turn gives

and hence the (2, -1, 2, 1) is a linear combination of the given vectors, with

step-by-step explanation:

just plug in each number for x and see which ones work and don't