Suppose u = (1,2,3), v = (2, -3, -4), and w = (1,0,-2). (a) find u-2v + 3w. (b) write the vector (3,4,5) as a linear combination of u, v, and w.

We are given vectors u,v and w as follows:

(a)

Now we are asked to find the value of:

The value is calculated as follows:

                              Hence,

(b)

We are asked to represent (3,4,5) as a linear combination of u, v, and w.

Let:

i.e.

on multiplying equation(1) by 2 an then adding equation (1) to equation (3)

on putting the value of a in equation (2) we get:

Now on putting the value of a and b in equation (1)

Hence, we have:

step-by-step explanation: