Answer:
To determine if the vector u is in the plane spanned by the columns of matrix A, we can check if u can be written as a linear combination of the columns of A. Let's calculate the linear combination:
u = 8 * [3, -2, 1] + (-4) * [-5, 4, 1] + 8 * [0, 1, 1]
Simplifying this expression, we get:
u = [24, -16, 8] + [20, -16, -4] + [0, 8, 8]
u = [44, -24, 12]
Now, we compare this result with the vector u given in the question:
u = [8, -4, 8]
Since [44, -24, 12] is not equal to [8, -4, 8], u is not in the plane spanned by the columns of A.
