Are the vectors 3 2 1 3 4 4 and 4 3 0 linearly independent I

Are the vectors [-3 2 1], [-3 4 -4] and [4 -3 0] linearly independent? If they are linearly dependent, find scalars that are not all zero such that the equation below is true. If they are linearly independent, find the only scalars that will make the equation below true. [-3 2 1]+ [-3 4 -4]+ [4 -3 0] = [0 0 0].

Solution

Your matrix

Find the pivot in the 1st column and swap the 3rd and the 1st rows

Eliminate the 1st column

Make the pivot in the 2nd column by dividing the 2nd row by 12

Eliminate the 2nd column

Make the pivot in the 3rd column by dividing the 3rd row by 1/4

Eliminate the 3rd column

solution

x1 = 0

x2 = 0

x3 = 0

all scalasr are zero linearly independent

	X1	X2	X3	b
1	-3	-3	4	0
2	2	4	-3	0
3	1	-4	0	0