Question

Determine if b is a linear combination of the vectors formed from the columns of the matrix a. Given a = [1 -2 -6, 0 3 7, 1 -2 5] and b = [11 -5 9], find if b is a linear combination of the vectors formed from the columns of a?

Answer 1

To determine if b is a linear combination of the vectors formed from the columns of matrix a, we can set up an augmented matrix and perform row operations to determine if it is consistent or inconsistent.

Step-by-step explanation:

To determine if b is a linear combination of the vectors formed from the columns of matrix a, we need to check if we can find coefficients that will satisfy the equation b = c1*a1 + c2*a2 + c3*a3, where a1, a2, and a3 are the columns of matrix a. Rearranging the equation, we have c1*a1 + c2*a2 + c3*a3 - b = 0. We can solve this system of equations by setting up the augmented matrix [a1 a2 a3 - b] and performing row operations to determine if it is consistent or inconsistent.

In this case, the matrix a = [1 -2 -6, 0 3 7, 1 -2 5] and the vector b = [11 -5 9]. We can set up the augmented matrix [1 0 1 11; -2 3 -2 -5; -6 7 5 9] and perform row operations to determine if it is consistent or inconsistent.