Let $A=\left(\begin{array}{cc}4 & -2 \\ \alpha & \beta\end{array}\right)$ If $A^2+\gamma A+18 l=0$, then $\operatorname{det}(A)$ is equal to _____.

JEE MATHEMATICS MCQ: MATRICES

1 Easy

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Application +4 | -1

Let

A=\left(\begin{array}{cc}4 & -2 \\ \alpha & \beta\end{array}\right)

A^2+\gamma A+18 l=0

, then

\operatorname{det}(A)

is equal to _____.

View answer and explanation

Correct option: B

Option B (18) is correct because by finding the characteristic equation and comparing it with the given equation, the determinant of A can be determined.

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\left|\begin{array}{ccc}1 & \left(\alpha^{2 x}-\alpha^{-2 x}\right)^2 & \left(\alpha^{2 x}+\alpha^{-2 x}\right)^2 \\ 1 & \left(\beta^{2 x}-\beta^{-2 x}\right)^2 & \left(\beta^{2 x}+\beta^{-2 x}\right)^2 \\ 1 & \left(\gamma^{2 x}-\gamma^{-2 x}\right)^2 & \left(\gamma^{2 x}+\gamma^{-2 x}\right)^2\end{array}\right|

, is If

\omega

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\left| {\begin{array}{cccccccccccccccccccc} 1&\omega &{{\omega ^2}}\\ \omega &{{\omega ^2}}&1\\ {{\omega ^2}}&1&\omega \end{array}} \right|

is equal to For any matrix

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, if

A(\operatorname{adj} A)=\left[\begin{array}{cc}10 & 0 \\ 0 & 10\end{array}\right]

, then

|A|

is equal to