Let $P=\left[a_{\|}\right]$be $a \times 3$ matrix and let $Q=\left[b_1\right]$, where $b_1=2^{1+j} a_{\|}$for $1 \leq i, j \leq 3$. If the determinant of $P$ is $2$ , then the determinant of the matrix $Q$ is

  • [IIT 2012]
  • A

    $2^{10}$

  • B

    $2^{11}$

  • C

    $2^{12}$

  • D

    $2^{13}$

Similar Questions

If $a,b,c$ are unequal what is the condition that the value of the following determinant is zero $\Delta = \left| {\,\begin{array}{*{20}{c}}a&{{a^2}}&{{a^3} + 1}\\b&{{b^2}}&{{b^3} + 1}\\c&{{c^2}}&{{c^3} + 1}\end{array}\,} \right|$

  • [IIT 1985]

Evaluate $\left|\begin{array}{ccc}\cos \alpha \cos \beta & \cos \alpha \operatorname{csin} \beta & -\sin \alpha \\ -\sin \beta & \cos \beta & 0 \\ \sin \alpha \cos \beta & \sin \alpha \sin \beta & \cos \alpha\end{array}\right|$

By using properties of determinants, show that:

$\left|\begin{array}{ccc}y+k & y & y \\ y & y+k & y \\ y & y & y+k\end{array}\right|=k^{2}(3 x+k)$

Which of the following matrices can $NOT$ be obtained from the matrix $\left[\begin{array}{cc}-1 & 2 \\ 1 & -1\end{array}\right]$ by a single elementary row operation?

  • [JEE MAIN 2022]

If $a, b, c > 0 \, and \, x, y, z \in R$ , then the determinant $\left|{\begin{array}{*{20}{c}}{{{\left( {{a^x}\, + \,\,{a^{ - x}}} \right)}^2}}&{{{\left( {{a^x}\, - \,\,{a^{ - x}}} \right)}^2}}&1\\{{{\left( {{b^y}\, + \,\,{b^{ - y}}} \right)}^2}}&{{{\left( {{b^y}\, - \,\,{b^{ - y}}} \right)}^2}}&1\\{{{\left( {{c^z}\, + \,\,{c^{ - z}}} \right)}^2}}&{{{\left( {{c^z}\, - \,\,{c^{ - z}}} \right)}^2}}&1\end{array}} \right|$ $=$