X ની કઈ કિંમત માટે :left[begin{array}{lll}1 & 2 & 1end{array}right

Hindi

3 and 4 .Determinants and Matrices

medium

$x$ ની કઈ કિંમત માટે $:\left[\begin{array}{lll}1 & 2 & 1\end{array}\right]\left[\begin{array}{lll}1 & 2 & 0 \\ 2 & 0 & 1 \\ 1 & 0 & 2\end{array}\right]\left[\begin{array}{l}0 \\ 2 \\ x\end{array}\right]=\mathrm{O} ?$

$-1$

Solution

We have $\left[\begin{array}{lll}1 & 2 & 1\end{array}\right]\left[\begin{array}{lll}1 & 2 & 0 \\ 2 & 0 & 1 \\ 1 & 0 & 2\end{array}\right]\left[\begin{array}{l}0 \\ 2 \\ x\end{array}\right]=0$

$\Rightarrow\left[\begin{array}{lll}1+4+1 & 2+0+0 & 0+2+2\end{array}\right]\left[\begin{array}{l}0 \\ 2 \\ x\end{array}\right]=0$

$\Rightarrow\left[\begin{array}{lll}6 & 2 & 4\end{array}\right]\left[\begin{array}{l}0 \\ 2 \\ x\end{array}\right]=0$

$\Rightarrow[6(0)+2(2)+4(x)]=0$

$\Rightarrow[4+4 x]=[0]$

$\therefore 4+4 x=0$

$\Rightarrow x=-1$

Thus, the required value of $x$ is $-1$

Standard 12

Mathematics

જો $A$ એ ચોરસ શ્રેણિક છે કે જેથી ${a_{ij}} \in \left\{ { – 1,0,1} \right\}\forall\,\, i,j$ અને દરેક હાર અને સ્તંભમાં માત્ર એકજ શૂન્યતર સંખ્યા હોય તો .. . .

hard

જો $A = \left[ {\begin{array}{*{20}{c}}{ – 1}&0&0\\0&{ – 1}&0\\0&0&{ – 1}\end{array}} \right]$, તો ${A^2}$ એ . . .

easy

જો $A + B = \left[ {\begin{array}{{20}{c}}1&0\\1&1\end{array}} \right]$ અને $A – 2B = \left[ {\begin{array}{{20}{c}}{ – 1}&1\\0&{ – 1}\end{array}} \right]\,,$ તો $A=$

easy

અહી $A=\left[a_{i j}\right]$ એ $3 \times 3$ શ્રેણિક છે કે જેથી $A \left[\begin{array}{l}0 \\ 1 \\ 0\end{array}\right]=\left[\begin{array}{l}0 \\ 0 \\ 1\end{array}\right], A \left[\begin{array}{l}4 \\ 1 \\ 3\end{array}\right]=\left[\begin{array}{l}0 \\ 1 \\ 0\end{array}\right]$ અને $A \left[\begin{array}{l}2 \\ 1 \\ 2\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$, તો $a _{23}$ ની કિમંત મેળવો.

hard

(JEE MAIN-2025)

જો $A = \left[ {\begin{array}{{20}{c}}1&3&0\\{ – 1}&2&1\\0&0&2\end{array}} \right],B = \left[ {\begin{array}{{20}{c}}2&3&4\\1&2&3\\{ – 1}&1&2\end{array}} \right]$, તો $AB =$

easy