Question

find the values of the parameters a and b such that the following linear system

a) will be inconsistent

b) will have infinitely many solutions

c) will have exactly one solution

3x-y+2z b +y-2z 0 2x-y+az 4

Answer 1

Kindly go through the solution and let me know in case of any doubt or further clarification is needed in the comment box.
Thanks for the question :)

ſ 8 -1 2 b ] Augmented Matrix of given lineae System [ 31 26 l i i2lol o Rz I RIJR2 log - - b la-i ai 4 R3 - ZR,R3 Lo 0 Q-2 3 676 P O R 3 + R2 R3 O then consistent & ber one solution then entintemmyst 12a=2 [ if a-2 & 0 then consiste S a 2 © 2-2=0 , 6716 then No Solutron -35*16= 0, b=16 ③ it a= 2 & b= 16 then Infinite many solution