Question

write v as a linear combination of u and w, if possible, where u = (2, 3) and w = (2, −1). (enter your answer in terms of u and w. if not possible, enter impossible.) v = (−4, −6)

Answer 1

To write v as a linear combination of u and w, we need to find coefficients a and b. By setting up the equation and solving for a and b, we find that v can be written as -2u + 0w.

Step-by-step explanation:

To write v as a linear combination of u and w, we need to find coefficients a and b such that av + bw = v. Let's set up the equation:

a(2, 3) + b(2, -1) = (-4, -6)

Expanding this equation, we get:

(2a + 2b, 3a - b) = (-4, -6)

Now we can solve for a and b by equating the corresponding components:

2a + 2b = -4

3a - b = -6

Solving these simultaneous equations gives a = -2 and b = 0. Therefore, v can be written as a linear combination of u and w as follows:

v = -2u + 0w