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 :
Solution
$$D = \left| {\matrix{
1 & 1 & 1 \cr
3 & 2 & 5 \cr
9 & 4 & {28 + [\lambda ]} \cr
} } \right| = - 24 - [\lambda ] + 15 = - [\lambda ] - 9$$<br><br>if $[\lambda ] + 9 \ne 0$ then unique solution<br><br>if $[\lambda ] + 9 = 0$ then D<sub>1</sub> = D<sub>2</sub> = D<sub>3</sub> = 0<br><br>so infinite solutions<br><br>Hence, $\lambda$ can be any red number.
About this question
Subject: Mathematics · Chapter: Matrices and Determinants · Topic: Types of Matrices and Operations
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