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3 and 4 .Determinants and Matrices

easy

यदि $A = \left[ {\begin{array}{*{20}{c}}1&1\\0&1\end{array}} \right]$, तो ${A^n} = $

$\left[ {\begin{array}{*{20}{c}}1&n\\0&1\end{array}} \right]$

$\left[ {\begin{array}{*{20}{c}}n&n\\0&n\end{array}} \right]$

$\left[ {\begin{array}{*{20}{c}}n&1\\0&n\end{array}} \right]$

$\left[ {\begin{array}{*{20}{c}}1&1\\0&n\end{array}} \right]$

Solution

(a) ${A^2} = \left[ {\begin{array}{*{20}{c}}1&1\\0&1\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}1&1\\0&1\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}1&2\\0&1\end{array}} \right],$

और ${A^3} = {A^2}.A = \left[ {\begin{array}{*{20}{c}}1&2\\0&1\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}1&1\\0&1\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}1&3\\0&1\end{array}} \right]$

==> ${A^n} = {A^{n – 1}}.A = \left[ {\begin{array}{*{20}{c}}1&{n – 1}\\0&1\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}1&1\\0&1\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}1&n\\0&1\end{array}} \right]$.

Std 12

Mathematics

मान लीजिए कि $A =\left[\begin{array}{ll}2 & 4 \\ 3 & 2\end{array}\right], B =\left[\begin{array}{cc}1 & 3 \\ -2 & 5\end{array}\right], C =\left[\begin{array}{cc}-2 & 5 \\ 3 & 4\end{array}\right],$ तो निम्नलिखित ज्ञात कीजिए:

$A+B$

easy

यदि $A = \left[ {\begin{array}{{20}{c}}{\cos \alpha }&{ – \sin \alpha }\\{\sin \alpha }&{\cos \alpha }\end{array}} \right]$ और $B = \left[ {\begin{array}{{20}{c}}{\cos \beta }&{ – \sin \beta }\\{\sin \beta }&{\cos \beta }\end{array}} \right]$, तो कौन सा सम्बन्ध सत्य है

medium

$AB = 0$, यदि और केवल यदि

normal

यदि $A = \left[ {\begin{array}{*{20}{c}}\lambda &1\\{ – 1}&{ – \lambda }\end{array}} \right]$, तो $\lambda $ के किस मान के लिये$\,{A^2} = 0$ है

easy

यदि $A =\left[\begin{array}{rr}3 & 1 \\ -1 & 2\end{array}\right]$ हो तो सिद्ध कीजिए कि $A ^{2}-5 A +7 I = O$ है।

medium

यदि $A = \left[ {\begin{array}{*{20}{c}}1&1\\0&1\end{array}} \right]$, तो ${A^n} = $

Solution

Similar Questions

मान लीजिए कि $A =\left[\begin{array}{ll}2 & 4 \\ 3 & 2\end{array}\right], B =\left[\begin{array}{cc}1 & 3 \\ -2 & 5\end{array}\right], C =\left[\begin{array}{cc}-2 & 5 \\ 3 & 4\end{array}\right],$ तो निम्नलिखित ज्ञात कीजिए: $A+B$

$AB = 0$, यदि और केवल यदि

यदि $A = \left[ {\begin{array}{*{20}{c}}\lambda &1\\{ – 1}&{ – \lambda }\end{array}} \right]$, तो $\lambda $ के किस मान के लिये$\,{A^2} = 0$ है

यदि $A =\left[\begin{array}{rr}3 & 1 \\ -1 & 2\end{array}\right]$ हो तो सिद्ध कीजिए कि $A ^{2}-5 A +7 I = O$ है।

मान लीजिए कि $A =\left[\begin{array}{ll}2 & 4 \\ 3 & 2\end{array}\right], B =\left[\begin{array}{cc}1 & 3 \\ -2 & 5\end{array}\right], C =\left[\begin{array}{cc}-2 & 5 \\ 3 & 4\end{array}\right],$ तो निम्नलिखित ज्ञात कीजिए:

$A+B$