Are the vectors 1 5 3 3 3 1 4 4 5 2 4 5 and 10 19 27 0 linea

Are the vectors [-1 5 -3 3], [-3 1 -4 -4], [-5 2 4 5] and [10 19 -27 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.

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 -14

Eliminate the 2nd column

Make the pivot in the 3rd column by dividing the 3rd row by 151/14

Eliminate the 3rd column

Solution set:

x1 = - 5x4

x2 = 0

x3 = 3x4

x4 - free

	X1	X2	X3	X4	b
1	-1	-3	-5	10	0
2	5	1	2	19	0
3	-3	-4	4	-27	0
4	3	-4	5	0	0