(6@) Let A= [ -8 -5 5] B= [4 2 -3] and C= [24 13 -17] Determine if the vectors a

Question

(6@)    

Let A= [ -8

             -5

              5]

B= [4

      2

      -3]

and C= [24

              13

              -17]

Determine if the vectors are linearly independent or linearly dependent. If they are linearly dependent, determine a non-trivial linear relation -(a                    non-trivial relation is three numbers which are not all three zeros) Otherwise, if the vectors are linearly independent, enter 0's for the coefficients, since                    the relationship always holds.                 

Write in this form: _____A + _____B+ _____C=0                 

Explain briefly why?

Explanation / Answer

let

A = k1B+k2C

=>(-8,-5,5) = k1*(4,2,-3) + k2*(24,13,-17)

=> 4k1+24k2 = -8

2k1+13k2 = -5

-3k1-17k2=5

k1 = 4 and k2 =-1 satifies above equations

therefore they are linearly dependent

and

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

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