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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
Let matrix $A = \left[ {\begin{array}{*{20}{c}}
  1&2&3 \\ 
  0&5&4 \\ 
  0&3&2 
\end{array}} \right]$ and $A^3 -8A^2 + \alpha A + \beta I = O$ then ordered pair $(\alpha , \beta)$ is
  • ✓
    $(5, 2)$
  • B
    $(5, -2)$
  • C
    $(-5, 2)$
  • D
    $(2, 5)$
✓

Answer

Correct option: A.
$(5, 2)$
a
$|A-\lambda I|=0$

$\Rightarrow \lambda^{3}-8 \lambda^{2}+5 \lambda+2=0$

$\Rightarrow A^{3}-8 A^{2}+5 A+2 I=0$

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