the answers is not zero Let A 3 4 2 1 B 3 2 1 1 and C 12

the answers is not zero

Let A = [-3 4 2 1], B = [-3 2 1 1], and C = [-12 10 9 1], and D = [-9 8 6 0]. Determine whether or not the three vectors listed above are linearly independent or linearly dependent. If they are linearly dependent, find a non-trivial linear combination with adds up to the zero vector. Otherwise, if the vectors are linearly independent, enter 0\'s for the coefficients. 0 A + 0 B + 0 C = 0 F = 0.

Solution

Your matrix

Find the pivot in the 1st column and swap the 4th and the 1st rows

Eliminate the 1st column

Find the pivot in the 2nd column (inversing the sign in the whole row) and swap the 3rd and the 2nd rows

Eliminate the 2nd column

Make the pivot in the 3rd column by dividing the 3rd row by -8

Eliminate the 3rd column

solution

x1 = - 2x4

x2 = (5/2)x4

x3 = - (1/2)x4

x4 - free

relation

- 4A + 5B - C + 2D = 0 (answer)

	X1	X2	X3	X4	b
1	-3	-3	-21	-9	0
2	4	2	10	8	0
3	2	1	9	6	0
4	1	1	1	0	0