Question

Let A = , let b = [10 3 7] , and let W be the set of all linear combinations of the columns of A. Is b in W?

Answer 1

To determine if vector b is in the set W, we need to check if there exist scalars that can form b as a linear combination of the columns of matrix A.

Step-by-step explanation:

The question asks whether the vector b = [10 3 7] is in the set W, which is defined as the set of all linear combinations of the columns of matrix A. To determine if b is in W, we need to check if there exist scalars k1, k2, and k3 such that b = k1 * column_1_of_A + k2 * column_2_of_A + k3 * column_3_of_A.

In this case, A is not provided, so it is not possible to directly verify if b is in W. To determine if b is in W, we need to find the column space of A, which is the set of all linear combinations of the columns of A. If b is in the column space of A, then it is in W.