Show the following vectors are linearly independent?

Question

(3,1,-1), (2,-1,7), (7,-1,23)

Answer 1

Check out their product of say

a x b x c

if the resulting vector is the null vector, they are linearly dependent; otherwise -- independent

Alternatively, if det (a,b,c) = 0 they are dependent, nonzero - independent.

OK, I'll do the determinant test:

3 1 -1
2 -1 7
7 -1 23

= -69 + 49 + 2 - (7 + 46 - 21)
= -50

independent

Answer 2

No. The 5th vector may well be expressed via potential of a linear mix of the a number of 4 self sustaining vectors. you ought to think of of in R3 and say any vector in r3 is a mix of i j ok vectors. So in accordance to danger say some element like there are certainly 4 perpendicular vectors in R4 only as there is definitely 3 in R3, 2 in R2, and one self sustaining vector in R1

Answer 3

If all else fails, you have three equations in three variables.

If the only solution is (0, 0, 0), you're done.

Answer 4

why dont u ask ur teacher whos teaching this crap to u

Answer 5

matlab
rref

Answer 6

no