Question

check the following vector linearly dependent x1=(1,2,1) x2=(2,1,4) x3=(4,5,6)​

Answer 1

Answer:

Step-by-step explanation:

Given vectors are $x_{1}$ =  (1,2,1) , $x_{2}$ = (2,1,4) and $x_{3}$ = (4,5,6)

We consider a linear equation

a $x_{1}$ + b $x_{2}$ = $x_{3}$   where a and b are constant.

⇔a(1,2,1) +b (2,1,4) = (4,5,6)

⇔(a,2a,a) + (2b,b,4b) = (4,5,6)

⇔(a+2b,2a+b,a+4b) = (4,5,6)

Therefore  a+2b = 4 ,

      2a+b= 5 ,

and a+4b = 6

From the above set of equations we get a = 2 and b = 1

Since we get the value of a and b so the vectors are linearly dependent.