Question

Determine if b is a linear combination of a1,a2,a3. a1 = (1,-2,0), a2 = (0,1,2), a3 = (5,-6,8), b = (2,-1,6)

Answer 1

To determine if vector b is a linear combination of vectors a1, a2, and a3, set up the equations and solve for the scalars k1, k2, and k3.

Step-by-step explanation:

To determine if vector b is a linear combination of vectors a1, a2, and a3, we need to check if there exist scalars k1, k2, and k3 such that b = k1*a1 + k2*a2 + k3*a3.

Let's set up the equations and solve for k1, k2, and k3.

For the x-coordinates: 2 = k1*1 + k2*0 + k3*5

For the y-coordinates: -1 = k1*(-2) + k2*1 + k3*(-6)

For the z-coordinates: 6 = k1*0 + k2*2 + k3*8

Solving these equations will give us the values of k1, k2, and k3, which will determine if b is a linear combination of a1, a2, and a3.