Question

Vector (1, K5) is a linear combination of (1.-3,2) and (2,-1,1) then k = ?
(a) K =-1
(b) K=-5
(c) K=-8
(d) K=8​

Answer 1

Answer:

x1+2x2=1

-3x1-x2=k

2x1+x2=5

on solving k=-8

so ans is -8

Step-by-step explanation:

Answer 2

Answer:

value of K = -8correct option is (c)

Step-by-step explanation:  

vector V= ( 1,K,5)

Given two vectors :    A = (1,-3,2)       B = (2,-1,1) V is linear combination of A and B

so V can be represented as  

V = α A + βB(1,K,5 ) = (α,-3α,2α) + ( 2β,-1β,1β)

 on comparing we  get

 α + 2β = 1 -------(i)

-3α -1β = K--------(ii)

 2α + β = 5--------(iii)

solving equation (i) and (iii)

 multiplying (i) by 2 and subtracting with (iii)

 2α + 4β = 2

- 2α -  β  = -5      

  3β = -3    

   β = -1 putting in (i)

 α =1-2β

  α = 1+2  

 α=3

substituting α and β in equation  (ii)

-3α -β = K-3

(3) - (-1) =K

K = -9 +1

K=-8