Let A 1 4 1 2 11 1 2 14 4 and b 7 33 0 Determine if b is a

Let A = [-1 4 1 -2 11 -1 -2 14 -4] and b = [7 -33 0]. Determine if b is a linear combination of a_1, a2_ and a_3, the columns of the matrix A. If it is a linear combination, determine a non-trivial linear relation - (a non-trivial relation is three numbers which are not all three zero.) Otherwise, enter 0\'s for the coefficients.

Solution

Your matrix

Find the pivot in the 1st column in the 1st row (inversing the sign in the whole row)

Eliminate the 1st column

Make the pivot in the 2nd column by dividing the 2nd row by 3

Eliminate the 2nd column

Solution set:

The system is inconsistent

	X1	X2	X3	b
1	-1	-2	-2	7
2	4	11	14	-33
3	1	-1	-4	0