the answers is not zero Let A 2 7 2 B 16 48 28 and C 2 5

the answers is not zero

Let A = [2 -7 2], B = [16 -48 28], and C = [2 -5 5]. 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 of A, B, C that adds up to 0. Otherwise, if the vectors are linearly independent, enter 0\'s for the coefficients. 0 A + 0 B + 0 C = 0.

Solution

Your matrix

Make the pivot in the 1st column by dividing the 1st row by 2

Eliminate the 1st column

Make the pivot in the 2nd column by dividing the 2nd row by 8

Eliminate the 2nd column

Hide solution

Solution set:

x1 = t

x2 = - (1/4)t

x3 = t ( free)

relation

A - (1/4)B + C = 0

or 4A - B +4C =0 (answer)

	X1	X2	X3	b
1	2	16	2	0
2	-7	-48	-5	0
3	2	28	5	0