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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