यदि A = left[ {begin{array}{*{20}{c}}{ab}&{{b^2}}{ - {a^2}}&{

English

Gujarati

Hindi

3 and 4 .Determinants and Matrices

medium

यदि $A = \left[ {\begin{array}{*{20}{c}}{ab}&{{b^2}}\\{ - {a^2}}&{ - ab}\end{array}} \right]$ और ${A^n} = O$, तो $n$ का न्यूनतम मान है

$2$

$3$

$4$

$5$

Solution

(a) ${A^2} = A.\,\,A = \left[ {\begin{array}{*{20}{c}}{ab}&{{b^2}}\\{ – {a^2}}&{ – ab}\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}{ab}&{{b^2}}\\{ – {a^2}}&{ – ab}\end{array}} \right]$

$ = \left[ {\begin{array}{*{20}{c}}{{a^2}{b^2} – {a^2}{b^2}}&{a{b^3} – a{b^3}}\\{ – {a^3}b + {a^3}b}&{ – {a^2}{b^2} + {a^2}{b^2}}\end{array}} \right] = O$

$ \Rightarrow \,\,{A^3} = A.{A^2} = 0$ व ${A^n} = 0$,$n \ge 2$ के प्रत्येक मान के लिए।

Standard 12

Mathematics

निदर्शित गुणनफल परिकलित कीजिए :$\left[\begin{array}{lll}2 & 3 & 4 \\ 3 & 4 & 5 \\ 4 & 5 & 6\end{array}\right]\left[\begin{array}{ccc}1 & -3 & 5 \\ 0 & 2 & 4 \\ 3 & 0 & 5\end{array}\right]$

easy

यदि $\left[ {\begin{array}{*{20}{c}}{2 + x}&3&4\\1&{ – 1}&2\\x&1&{ – 5}\end{array}} \right]$अव्युत्क्रमणीय आव्यूह हो, तो $x$ का मान होगा

easy

यदि $A + B = \left[ {\begin{array}{{20}{c}}1&0\\1&1\end{array}} \right]$ और $A – 2B = \left[ {\begin{array}{{20}{c}}{ – 1}&1\\0&{ – 1}\end{array}} \right]\,,$ तो $A=$

easy

यद् $A =\left[\begin{array}{ccc}\frac{2}{3} & 1 & \frac{5}{3} \\ 1 & 2 & 4 \\ 3 & 3 & 3 \\ \frac{7}{3} & 2 & \frac{2}{3}\end{array}\right]$ तथा $B =\left[\begin{array}{ccc}\frac{2}{5} & \frac{3}{5} & 1 \\ 1 & 2 & 4 \\ 5 & 5 & 5 \\ \frac{7}{5} & \frac{6}{5} & \frac{2}{5}\end{array}\right],$ तो $3 A -5 B$ परिकलित कीजिए

medium

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

easy

यदि $A = \left[ {\begin{array}{*{20}{c}}{ab}&{{b^2}}\\{ - {a^2}}&{ - ab}\end{array}} \right]$ और ${A^n} = O$, तो $n$ का न्यूनतम मान है

Solution

Similar Questions

निदर्शित गुणनफल परिकलित कीजिए :$\left[\begin{array}{lll}2 & 3 & 4 \\ 3 & 4 & 5 \\ 4 & 5 & 6\end{array}\right]\left[\begin{array}{ccc}1 & -3 & 5 \\ 0 & 2 & 4 \\ 3 & 0 & 5\end{array}\right]$

यदि $\left[ {\begin{array}{*{20}{c}}{2 + x}&3&4\\1&{ – 1}&2\\x&1&{ – 5}\end{array}} \right]$अव्युत्क्रमणीय आव्यूह हो, तो $x$ का मान होगा

यदि $A + B = \left[ {\begin{array}{*{20}{c}}1&0\\1&1\end{array}} \right]$ और $A – 2B = \left[ {\begin{array}{*{20}{c}}{ – 1}&1\\0&{ – 1}\end{array}} \right]\,,$ तो $A=$

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

Start a Free Trial Now

यदि $A + B = \left[ {\begin{array}{{20}{c}}1&0\\1&1\end{array}} \right]$ और $A – 2B = \left[ {\begin{array}{{20}{c}}{ – 1}&1\\0&{ – 1}\end{array}} \right]\,,$ तो $A=$