Consider the following system of equations: x + 2 y - 3 z = a 2 x + 6 y - 11 z = b x - 2 y + 7 z = c where a…

Consider the following system of equations: 

x+2y-3z=a

2x+6y-11z=b

x-2y+7z=c

where a,b and c are real constants. Then the system of equations :

  1. has a unique solution when 5a=2b+c
  2. has no solution for all a,b and c
  3. has infinite number of solutions when 5a=2b+c
  4. has a unique solution for all a,b and c

Solution

D=12-326-111-27

=20-2(25)-3(-10)

=20-50+30=0

D1=a2-3b6-11c-27

=20a-2(7b+11c)-3(-2b-6c)

=20a-14b-22c+6b+18c

=20a-8b-4c

=4(5a-2b-c)

D2=1a-32b-111c7

=7b+11c-a(25)-3(2c-b)

=7b+11c-25a-6c+3b

=-25a+10b+5c

=-5(5a-2b-c)

D3=12a26b1-2c

=6c+2b-2(2c-b)-10a

=-10a+4b+2c

=-2(5a-2b-c) 

for infinite solution

D=D1=D2=D3=0

⇒5a=2b+c

Asked in: JEE Main 2021 (26 Feb Shift 2)

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