Mathematics · 2018
JEE Main · 15 April 2018, Shift 2 · Q64
Suppose A is any 3 × 3 non-singular matrix and ( A -3 I )( A -5 I )= O, where I = I_3 and O = O_3. If α A +β A^-1=4 I, then α+β is equal to:
Suppose A is any $\displaystyle 3$ × $\displaystyle 3$ non-singular matrix and $\displaystyle (\mathrm{A}-3 \mathrm{I})(\mathrm{A}-5 \mathrm{I})=\mathrm{O}$, where $\displaystyle \mathrm{I}=\mathrm{I}_3$ and $\displaystyle \mathrm{O}=\mathrm{O}_3$. If $\displaystyle \alpha \mathrm{A}+\beta \mathrm{A}^{-1}=4 \mathrm{I}$, then $\displaystyle \alpha+\beta$ is equal to :
Official answer
(1)
$\displaystyle 8$
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JEE Main 2018 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.