Question

Determine a condição para constante de K para que o conjunto B={(-1,1,-3,4,1), (1,0,-1,2,-3), (1,-2,5,2,7), (2,-1,1,k,-1) R⁵ seja linearmente dependente.​

Answer 1

Resposta:

(2,-1,1,k,-1) =a*(-1,1,-3,4,1) +b*(1,0,-1,2,-3)+c*(1,-2,5,2,7)

2= -a+b+c  ==>a=b+c-2  (i)

-1=a-2c   (ii)

1= -3a-b+5c   (iii)

(i) em (ii)

-1=b+c-2 -2c ==> c =b-1 (iv)

(i) em (iii)

1=-3*(b+c-2)-b+5c

1=-3b-3c+6-b+5c

0=-4b+2c+5  ==>c=(4b-5)/2  (v)

(iv)=(v)

b-1=(4b-5)/2

2b-2=4b-5  ==>2b=3  ==>b=3/2

usando (iv) c=3/2-1=1/2

usando (i)  a=3/2+1/2-2=0

a=0

b=3/2

c=1/2

k=4a+2b+2c  

k=4*(0) +2*3/2 +2*(1/2)

k=4  

Para k=4   o conjunto B será LD