Question

$2x-y-2z=2,x-2y+z=-4,x+y+\lambda z=4$ then the value of $\lambda$ such that system of equations has no solution, is

• A. $1$
• B. $2$
• C. $3$
• D. $-3$

Answer 1

Answer: (A)

$1$

(a) Here $△=\left|\begin{array}{ccc}1& 4& -2\\ 3& 1& 5\\ 2& 3& 1\end{array}\right|$

=$1(1-15)-3(4+6)+2(20+2)$

= $-14-30+44=0$

And ${△}_x=\left|\begin{array}{ccc}3& 4& -2\\ 7& 1& 5\\ 5& 3& 1\end{array}\right|=3(1-15)-7(4+6)+5(20+2)=-2\ne 0$
Since $△=0$ and ${△}_x\ne 0$, the equations are not consistent and hence there is no solution of the given system of equations.