यदि left[ {begin{array}{*{20}{c}}1&2&33&1&22&3&1end{array}} right],lef

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3 and 4 .Determinants and Matrices

easy

यदि$\left[ {\begin{array}{{20}{c}}1&2&3\\3&1&2\\2&3&1\end{array}} \right]\,\left[ \begin{array}{l}x\\y\\z\end{array} \right] = \left[ {\begin{array}{{20}{c}}4&{ - 2}\\0&{ - 6}\\{ - 1}&2\end{array}} \right]\,\left[ \begin{array}{l}2\\1\end{array} \right]$, तो $(x,y,z)$=

$( - 4,\,2,\,2)$

$(4,\, - 2,\, - 2)$

$(4,\,2,\,2)$

$( - 4,\, - 2,\, - 2)$

Solution

(a) $\left[ {\begin{array}{*{20}{c}}1&2&3\\3&1&2\\2&3&1\end{array}} \right]\,\,\left[ \begin{array}{l}x\\y\\z\end{array} \right] = \left[ {\begin{array}{*{20}{c}}4\\0\\{ – 1}\end{array}\,\,\begin{array}{*{20}{c}}{ – 2}\\{ – 6}\\2\end{array}} \right]\,\left[ \begin{array}{l}2\\1\end{array} \right]\,$

$\begin{array}{l}\,\,\,\,\,\,\,\,\,\,\,\,\,x + 2y + 3z = 6\\\, \Rightarrow \,\,\,\,\,3x + y + 2z = – \,6\\\,{\rm{ }}2x + 3y + z = 0\end{array}$

समीकरणों को हल करने पर,

$x = – 4,\,y = 2,\,z = 2$.

Standard 12

Mathematics

माना I, कोटि $2 \times 2$ का तत्समक आव्यूह है तथा $P =\left[\begin{array}{rr}2 & -1 \\ 5 & -3\end{array}\right]$ है। तो $n \in N$ का वह मान, जिसके लिए $Pn =5 I -8 P$ है, बराबर है

medium

(JEE MAIN-2021)

यदि $A =\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]$ है तो सिद्ध कीजिए कि $A ^{n}=\left[\begin{array}{cc}\cos n \theta & \sin n \theta \\ -\sin n \theta & \cos n \theta\end{array}\right], n \in N$

hard

यदि $AB = C$, तो आव्यूह $A,B,C$हैं

easy

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

easy

यदि$A = \left[ {\begin{array}{{20}{c}}2&5\\3&7\end{array}} \right]$and $B = \left[ {\begin{array}{{20}{c}}0&3\\4&1\end{array}} \right],$ तब

easy

यदि$\left[ {\begin{array}{*{20}{c}}1&2&3\\3&1&2\\2&3&1\end{array}} \right]\,\left[ \begin{array}{l}x\\y\\z\end{array} \right] = \left[ {\begin{array}{*{20}{c}}4&{ - 2}\\0&{ - 6}\\{ - 1}&2\end{array}} \right]\,\left[ \begin{array}{l}2\\1\end{array} \right]$, तो $(x,y,z)$=

Solution

Similar Questions

माना I, कोटि $2 \times 2$ का तत्समक आव्यूह है तथा $P =\left[\begin{array}{rr}2 & -1 \\ 5 & -3\end{array}\right]$ है। तो $n \in N$ का वह मान, जिसके लिए $Pn =5 I -8 P$ है, बराबर है

यदि $A =\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]$ है तो सिद्ध कीजिए कि $A ^{n}=\left[\begin{array}{cc}\cos n \theta & \sin n \theta \\ -\sin n \theta & \cos n \theta\end{array}\right], n \in N$

यदि $AB = C$, तो आव्यूह $A,B,C$हैं

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

यदि$A = \left[ {\begin{array}{*{20}{c}}2&5\\3&7\end{array}} \right]$and $B = \left[ {\begin{array}{*{20}{c}}0&3\\4&1\end{array}} \right],$ तब

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यदि$\left[ {\begin{array}{{20}{c}}1&2&3\\3&1&2\\2&3&1\end{array}} \right]\,\left[ \begin{array}{l}x\\y\\z\end{array} \right] = \left[ {\begin{array}{{20}{c}}4&{ - 2}\\0&{ - 6}\\{ - 1}&2\end{array}} \right]\,\left[ \begin{array}{l}2\\1\end{array} \right]$, तो $(x,y,z)$=

यदि$A = \left[ {\begin{array}{{20}{c}}2&5\\3&7\end{array}} \right]$and $B = \left[ {\begin{array}{{20}{c}}0&3\\4&1\end{array}} \right],$ तब