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

(x, y) -> (x + 1, y + 1), (x, y) -> (y, x)

Step-by-step explanation:

I'll use point B (-3,0) for this problem.

First, the translation rule tells us to add 1 to the x value and add 1 to the y value. Now we have (-2, 1). Next, the rule tells us to flip the x and y coordinates. Now we have (1, -2). This matches to vertex B''(1, -2).