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3 and 4 .Determinants and Matrices
medium
સમીકરણની સંહતિ $3x - 2y + z = 0$, $\lambda x - 14y + 15z = 0$, $x + 2y - 3z = 0$ ને $x = y = z = 0$ સિવાયનો ઉકેલ હોય તો $\lambda $ મેળવો.
A
$1$
B
$2$
C
$3$
D
$5$
Solution
(d) The system of equations has infinitely many (non-trivial) solution,
if $\Delta = 0$ i.e., if $\left| {\,\begin{array}{*{20}{c}}3&{ – 2}&1\\\lambda &{ – 14}&{15}\\1&2&{ – 3}\end{array}\,} \right| = 0$
==> $3(42 – 30) – \lambda (6 – 2) + 1( – 30 + 14) = 0$
==> $\lambda = 5$ .
Standard 12
Mathematics
