Question

If system of linear equations $(a-1) x+z=\alpha, x+(b-1) y=\beta$ and $y+(c-1) z=\gamma$ where $a, b, c \in I$ does not have a unique solution, then maximum possible value of $|a+b+c|$ is

• A. 0
• B. 1
• C. 3
• D. 4

Answer 1

Answer: (D)

$(a-1) x+0 y+z=\alpha $ ....(1)
$x+(b-1) y+0 z=\beta $....(2)
$0 x+y+(c-1) z=\gamma$....(3)
For no unique solution $D =0$
$\begin{vmatrix}(a-1) & 0 & 1 \\1 & (b-1) & 0 \\0 & 1 & (c-1)\end{vmatrix}=0 $
$(a-1)(b-1)(c-1)+1=0 $
$\therefore a=2 ; b=2 ; c=0$
Hence, $| a + b + c |=4$.