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3 and 4 . determinant and metrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths3 and 4 . determinant and metrices1 Mark
MCQ
If $R(t) = \left[ {\begin{array}{*{20}{c}}{\cos t}&{\sin t}\\{ - \sin t}&{\cos t}\end{array}} \right],$then $R(s).\,R(t) = $
  • A
    $R(s) + R(t)$
  • B
    $R\,(st)$
  • ✓
    $R(s + t)$
  • D
    None of these
✓

Answer

Correct option: C.
$R(s + t)$
c
(c) $R(s)\,R(t) = \left[ {\begin{array}{*{20}{c}}{\cos s}&{\sin s}\\{ - \sin s}&{\cos s}\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}{\cos t}&{\sin t}\\{ - \sin t}&{\cos t}\end{array}} \right]$

= $\left[ {\begin{array}{*{20}{c}}{\cos (s + t)}&{\sin (t + s)}\\{ - \sin (s + t)}&{\cos (t + s)}\end{array}} \right] = R(s + t)$.

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