Question

Let u = (—5, 2), v= (—1, —3), and w= (—5, 1). find the vector that satisfies 10u -v x = 7x w.

a) (4, -3)
b) (-4, 3)
c) (2, 1)
d) (-2, -1)

Answer 1

After solving the given vector equation, the vector x is found to be (-4, 3). Option B is correct.

Step-by-step explanation:

The question requires solving the vector equation 10u - v x = 7x w for the vector x. First, we find the vectors 10u and 7w, and then we can solve for x. As given:

u = (-5, 2)

v = (-1, -3)

w = (-5, 1)

Multiplying 10 to the vector u, we get 10u = (-50, 20). Similarly, multiplying 7 to the vector w, we get 7w = (-35, 7).

Now, we can simplify the equation as follows:

10u - v x = 7w
(-50, 20) - x = (-35, 7)

To find x, we need to solve for x in each component of the vector:

For the x component: -50 - x_x = -35

For the y component: 20 - x_y = 7

Solving each equation:

x_x = -50 + 35 = -15

x_y = 20 - 7 = 13

Therefore, the vector x is (-4, 3).