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3 and 4 .Determinants and Matrices
easy
જો $R(t) = \left[ {\begin{array}{*{20}{c}}{\cos t}&{\sin t}\\{ - \sin t}&{\cos t}\end{array}} \right],$ તો $R(s).\,R(t) = $
A
$R(s) + R(t)$
B
$R\,(st)$
C
$R(s + t)$
D
એકપણ નહી.
Solution
(c) $R(s)\,R(t) = \left[ {\begin{array}{*{20}{c}}{\cos s}&{\sin s}\\{ – \sin s}&{\cos s}\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}{\cos t}&{\sin t}\\{ – \sin t}&{\cos t}\end{array}} \right]$
= $\left[ {\begin{array}{*{20}{c}}{\cos (s + t)}&{\sin (t + s)}\\{ – \sin (s + t)}&{\cos (t + s)}\end{array}} \right] = R(s + t)$.
Standard 12
Mathematics
