3 and 4 .Determinants and Matrices
normal

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

A

$(5, 2)$

B

$(5, -2)$

C

$(-5, 2)$

D

$(2, 5)$

Solution

$|A-\lambda I|=0$

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

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

Standard 12
Mathematics

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