Question

For what value of $\lambda ,$ the system of equations $x+y+z=6,x+2y+3z=10,$ $x+2y+\lambda z=10$ is consistent?

• A. 1
• B. 2
• C. $-1$
• D. 3
• E. $-3$

Answer 1

Answer: (D)

The system of equations is consistent, if $\left|\begin{array}{ccc}1& 1& 1\\ 1& 2& 3\\ 1& 2& \lambda \end{array}\right|=0$ $\Rightarrow$ $\lambda =3$