Question

Investigate for the values of $\lambda =3,\mu =10$ the simultaneous equations $x+y+z=6;x+2y+3z=10$ & $x+2y+\lambda z=\mu$ have;

• A. A unique solution
• B. An infinite number of solutions
• C. No solution
• D. All of the above

Answer 1

Answer: (B)

An infinite number of solutions

Unique solution

$\left|\begin{array}{ccc}1& 1& 1\\ 1& 2& 3\\ 1& 2& 2\end{array}\right|\ne 0$

$\left|1\right(2\lambda -6)-1(\lambda -3)+1(2-2\left)\right|\ne 0$

$2\lambda -6-\lambda +3\ne 0$

$\lambda \ne 3$ -unique solution

$\lambda =3,\mu =10$, infinite solution

$\lambda =3,\mu \ne 10$,-no solution