Let [[]] be the greatest integer less than or equal to [].

Question

Let [$$\lambda$$] be the greatest integer less than or equal to $$\lambda$$. The set of all values of $$\lambda$$ for which the system of linear equations
x + y + z = 4,
3x + 2y + 5z = 3,
9x + 4y + (28 + [$$\lambda$$])z = [$$\lambda$$] has a solution is :

Accepted Answer

$$D = \left| {\begin{pmatrix} 1 & 1 & 1  \
   3 & 2 & 5  \
   9 & 4 & {28 + [\lambda ]}  \

\end{pmatrix} } \right| =  - 24 - [\lambda ] + 15 =  - [\lambda ] - 9$$

if $$[\lambda ] + 9 \ne 0$$ then unique solution

if $$[\lambda ] + 9 = 0$$ then D1 = D2 = D3 = 0

so infinite solutions

Hence, $$\lambda$$ can be any red number.

Solutions · 1