यदि किसी आव्यूह में 8 अवयव हैं, तो इसकी ?

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3 and 4 .Determinants and Matrices

easy

यदि किसी आव्यूह में $8$ अवयव हैं, तो इसकी संभव कोटियाँ क्या हो सकती हैं?

Option A

Option B

Option C

Option D

Solution

We know that if a matrix is of order $m \times n,$ it has $mn$ elements. Thus, to find all possible orders of a matrix with $8$ elements, we will find all ordered pairs of natural numbers, whose product is $8$ .

Thus, all possible ordered pairs are $(1,8),\,(8,1),\,(4,2),\,(2,4)$

Hence, possible orders are $1 \times 8$ , $8 \times 1$, $4 \times 2$ , $2 \times 4$

Standard 12

Mathematics

यदि $A = \left[ {\begin{array}{{20}{c}}1&2\\{ – 3}&0\end{array}} \right]$ और $B = \left[ {\begin{array}{{20}{c}}{ – 1}&0\\2&3\end{array}} \right]$, तो

easy

यदि $A =\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1\end{array}\right],$ तो सिद्ध कीजिए कि $A ^{n}=\left[\begin{array}{lll}3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1}\end{array}\right], n \in N$

medium

$X$ तथा $Y$ ज्ञात कीजिए यदि $Y =\left[\begin{array}{ll}3 & 2 \\ 1 & 4\end{array}\right]$ तथा $2 X + Y =\left[\begin{array}{rl}1 & 0 \\ -3 & 2\end{array}\right]$

medium

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 $(x,y,z)$=

easy

यदी $A =\left[\begin{array}{rrr}1 & -2 & 3 \\ -4 & 2 & 5\end{array}\right]$ और $B =\left[\begin{array}{ll}2 & 3 \\ 4 & 5 \\ 2 & 1\end{array}\right],$ तो $AB$ तथा $BA$ ज्ञात कीजिए। दर्शाइए कि $AB \neq BA$

medium

यदि किसी आव्यूह में $8$ अवयव हैं, तो इसकी संभव कोटियाँ क्या हो सकती हैं?

Solution

Similar Questions

यदि $A = \left[ {\begin{array}{*{20}{c}}1&2\\{ – 3}&0\end{array}} \right]$ और $B = \left[ {\begin{array}{*{20}{c}}{ – 1}&0\\2&3\end{array}} \right]$, तो

यदि $A =\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1\end{array}\right],$ तो सिद्ध कीजिए कि $A ^{n}=\left[\begin{array}{lll}3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1}\end{array}\right], n \in N$

$X$ तथा $Y$ ज्ञात कीजिए यदि $Y =\left[\begin{array}{ll}3 & 2 \\ 1 & 4\end{array}\right]$ तथा $2 X + Y =\left[\begin{array}{rl}1 & 0 \\ -3 & 2\end{array}\right]$

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 $(x,y,z)$=

यदी $A =\left[\begin{array}{rrr}1 & -2 & 3 \\ -4 & 2 & 5\end{array}\right]$ और $B =\left[\begin{array}{ll}2 & 3 \\ 4 & 5 \\ 2 & 1\end{array}\right],$ तो $AB$ तथा $BA$ ज्ञात कीजिए। दर्शाइए कि $AB \neq BA$

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यदि $A = \left[ {\begin{array}{{20}{c}}1&2\\{ – 3}&0\end{array}} \right]$ और $B = \left[ {\begin{array}{{20}{c}}{ – 1}&0\\2&3\end{array}} \right]$, तो

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 $(x,y,z)$=