If $A=\left[\begin{array}{ll}1 & 2 \\ 4 & 2\end{array}\right],$ then show that $|2 A|=4|A|$.
If $A=\left[\begin{array}{ll}1 & 2 \\ 4 & 2\end{array}\right],$ then show that $|2 A|=4|A|$.
The given matrix is $A=\left[\begin{array}{ll}1 & 2 \\ 4 & 2\end{array}\right]$
$\therefore 2 A=2\left[\begin{array}{ll}1 & 2 \\ 4 & 2\end{array}\right]=\left[\begin{array}{ll}2 & 4 \\ 8 & 4\end{array}\right]$
$\begin{aligned} L H S:|2 A| &=\left|\begin{array}{ll}2 & 4 \\ 8 & 4\end{array}\right| \\ &=2 \times 4-4 \times 8 \\ &=8-32=-24 \end{aligned}$
Now, $|A|=\left[\begin{array}{ll}1 & 2 \\ 4 & 2\end{array}\right]=1 \times 2-2 \times 4=2 \times 8=-6$
$R H S: 4|A|=4 \times(-6)=-24$
$\therefore L. H. S.=\therefore \mathrm{R.} \mathrm{H.} \mathrm{S}$
Similar Questions
If $\mathrm{a}_{\mathrm{r}}=\cos \frac{2 \mathrm{r} \pi}{9}+i \sin \frac{2 \mathrm{r} \pi}{9}, \mathrm{r}=1,2,3, \ldots, i=\sqrt{-1}$ then the determinant $\left|\begin{array}{lll}a_{1} & a_{2} & a_{3} \\ a_{4} & a_{5} & a_{6} \\ a_{7} & a_{8} & a_{9}\end{array}\right|$ is equal to :
If $\mathrm{a}_{\mathrm{r}}=\cos \frac{2 \mathrm{r} \pi}{9}+i \sin \frac{2 \mathrm{r} \pi}{9}, \mathrm{r}=1,2,3, \ldots, i=\sqrt{-1}$ then the determinant $\left|\begin{array}{lll}a_{1} & a_{2} & a_{3} \\ a_{4} & a_{5} & a_{6} \\ a_{7} & a_{8} & a_{9}\end{array}\right|$ is equal to :
- [JEE MAIN 2021]
If $\alpha , \beta \, and \, \gamma$ are real numbers , then $D = \left|{\begin{array}{*{20}{c}}1&{\cos \,(\beta \, - \,\alpha )}&{\cos \,(\gamma \, - \,\alpha )}\\{\cos \,(\alpha \, - \,\beta )}&1&{\cos \,(\gamma \, - \,\beta )}\\{\cos \,(\alpha \, - \,\gamma )}&{\cos \,(\beta \, - \,\gamma )}&1 \end{array}} \right|$ =
If $\alpha , \beta \, and \, \gamma$ are real numbers , then $D = \left|{\begin{array}{*{20}{c}}1&{\cos \,(\beta \, - \,\alpha )}&{\cos \,(\gamma \, - \,\alpha )}\\{\cos \,(\alpha \, - \,\beta )}&1&{\cos \,(\gamma \, - \,\beta )}\\{\cos \,(\alpha \, - \,\gamma )}&{\cos \,(\beta \, - \,\gamma )}&1 \end{array}} \right|$ =
$\left| {\,\begin{array}{*{20}{c}}{13}&{16}&{19}\\{14}&{17}&{20}\\{15}&{18}&{21}\end{array}\,} \right| = $
$\left| {\,\begin{array}{*{20}{c}}{13}&{16}&{19}\\{14}&{17}&{20}\\{15}&{18}&{21}\end{array}\,} \right| = $
If $a \ne b \ne c,$ the value of $x$ which satisfies the equation $\left| {\,\begin{array}{*{20}{c}}0&{x - a}&{x - b}\\{x + a}&0&{x - c}\\{x + b}&{x + c}&0\end{array}\,} \right| = 0$, is
If $a \ne b \ne c,$ the value of $x$ which satisfies the equation $\left| {\,\begin{array}{*{20}{c}}0&{x - a}&{x - b}\\{x + a}&0&{x - c}\\{x + b}&{x + c}&0\end{array}\,} \right| = 0$, is
The number of solutions of equations $x + y - z = 0$, $3x - y - z = 0, \,x - 3y + z = 0$ is
The number of solutions of equations $x + y - z = 0$, $3x - y - z = 0, \,x - 3y + z = 0$ is