1)

If x=a  ,y=b,z=c is the solutions of the system of simultaneous linear equations x+y+z=4 , x-y+z=2 , x+2y+2z=1 , then ab+bc+ca=


A) 0

B) -25

C) 1

D) -4

Answer:

Option B

Explanation:

Given that,

x+y+z=4, x-y+z=2 and x+2y+2z=1

= [111111122]=1(22)1(21)+(2+1)]

  =  -4-1+3=2

1=[411111122]=4(22)1(41)+1(4+1)

  =4(4)3+5=163+5=14

2=[141121112]

2=1(41)4(21)+1(12)=341=2

3=[114112121]

3=  1(-1-4)-1(1-2)+4(2+1)=(-5)+1+12=8$

 x=1=142=7, y=2=22=1

and z=3=82=4

 So, a=7, b=1, c=-4

Now, ab+bc+ca

 = 7(1)+1(4)+(4)(7)=7428=25