જો P=left[begin{array}{ll}1 & 0 1 / 2 & 1end{array}right] તો P^{50} મેળવો.

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3 and 4 .Determinants and Matrices

medium

જો $P=\left[\begin{array}{ll}1 & 0 \\ 1 / 2 & 1\end{array}\right]$ તો $P^{50}$ મેળવો.

$\left[\begin{array}{cc}1 & 25 \\ 0 & 1\end{array}\right]$

$\left[\begin{array}{ll}1 & 0 \\ 25 & 1\end{array}\right]$

$\left[\begin{array}{ll}1 & 0 \\ 50 & 1\end{array}\right]$

$\left[\begin{array}{cc}1 & 50 \\ 0 & 1\end{array}\right]$

(JEE MAIN-2021)

Solution

$P=\left[\begin{array}{cc}1 & 0 \\ \frac{1}{2} & 1\end{array}\right]$

$P^{2}=\left[\begin{array}{ll}1 & 0 \\ \frac{1}{2} & 1\end{array}\right]\left[\begin{array}{ll}1 & 0 \\ \frac{1}{2} & 1\end{array}\right]=\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right]$

$P^{3}=\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right]\left[\begin{array}{cc}1 & 0 \\ \frac{1}{2} & 1\end{array}\right]=\left[\begin{array}{cc}1 & 0 \\ \frac{3}{2} & 1\end{array}\right]$

$P^{4}=\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right]\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right]=\left[\begin{array}{ll}1 & 0 \\ 2 & 1\end{array}\right]$

$\vdots$

$\therefore P^{50}=\left[\begin{array}{cc}1 & 0 \\ 25 & 1\end{array}\right]$

Standard 12

Mathematics

સાબિત કરો કે, $\left[ {\begin{array}{{20}{c}}
5&{ – 1} \\
6&7
\end{array}} \right]\left[ {\begin{array}{{20}{l}}
2&1 \\
3&4
\end{array}} \right]$ $ \ne \left[ {\begin{array}{{20}{l}}
2&1 \\
3&4
\end{array}} \right]\left[ {\begin{array}{{20}{l}}
5&{ – 1} \\
6&7
\end{array}} \right]$

medium

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

easy

એક ચોરસ શ્રેણિકની કક્ષા $5$ એકમ છે કે જેથી ${a_{ij}} = 0\,\,\forall \,\,i + j\, = n + 1,\,a_{ij}\, \in \left\{ {0,1} \right\}\,\,\forall \,\,i,j$. અને જો દરેક હાર અને સ્તંભમાં માત્ર એકજ શૂન્યતર ઘટક હોય તો આવા શ્રેણિક ની સંખ્યા મેળવો.

normal

$A=\left[\begin{array}{ll}2 & 4 \\ 3 & 2\end{array}\right], B=\left[\begin{array}{cc}1 & 3 \\ -2 & 5\end{array}\right], C=\left[\begin{array}{cc}-2 & 5 \\ 3 & 4\end{array}\right]$ હોય, તો $A+B$ મેળવો

easy

જો $A=\left[\begin{array}{ll}3 & -2 \\ 4 & -2\end{array}\right]$ અને $I=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right],$ હોય, તો એવો $k$ શોધો કે જેથી $A^{2}=k A-2 I$ થાય.

medium

જો $P=\left[\begin{array}{ll}1 & 0 \\ 1 / 2 & 1\end{array}\right]$ તો $P^{50}$ મેળવો.

Solution

Similar Questions

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

$A=\left[\begin{array}{ll}2 & 4 \\ 3 & 2\end{array}\right], B=\left[\begin{array}{cc}1 & 3 \\ -2 & 5\end{array}\right], C=\left[\begin{array}{cc}-2 & 5 \\ 3 & 4\end{array}\right]$ હોય, તો $A+B$ મેળવો

જો $A=\left[\begin{array}{ll}3 & -2 \\ 4 & -2\end{array}\right]$ અને $I=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right],$ હોય, તો એવો $k$ શોધો કે જેથી $A^{2}=k A-2 I$ થાય.

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