- Home
- Standard 12
- Mathematics
3 and 4 .Determinants and Matrices
hard
ધારોકે $\alpha \beta \neq 0$ અને $\mathrm{A}=\left[\begin{array}{rrr}\beta & \alpha & 3 \\ \alpha & \alpha & \beta \\ -\beta & \alpha & 2 \alpha\end{array}\right]$. જો $B=\left[\begin{array}{rrr}3 \alpha & -9 & 3 \alpha \\ -\alpha & 7 & -2 \alpha \\ -2 \alpha & 5 & -2 \beta\end{array}\right]$ એ $A$ ના ઘટકોના સહઅવયવો નો શ્રેણિક હોય, તો $\operatorname{det}(A B)=$ ............
A
$343$
B
$125$
C
$64$
D
$216$
(JEE MAIN-2024)
Solution
Equating co-factor fo $\mathrm{A}_{21}$
$ \left(2 \alpha^2-3 \alpha\right)=\alpha $
$ \alpha=0,2 \text { (accept) }$
Now, $2 \alpha^2-\alpha \beta=3 \alpha$
$ \alpha=2 \quad \beta=1 $
$ |A B|=|A \operatorname{cof}(A)|=|A|^3$
$A=\left|\begin{array}{ccc}1 & 2 & 3 \\ 2 & 2 & 1 \\ -1 & 2 & 4\end{array}\right|=6-2(9)+3(6)=6$
Standard 12
Mathematics
