यद् A =left[begin{array}{ccc}frac{2}{3} & 1 & frac{5}{3} 1 & 2 & 4 3 & 3 &

Hindi

3 and 4 .Determinants and Matrices

medium

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

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

Solution

$3A – 5B = $ $3\left[ {\begin{array}{*{20}{l}}
{\frac{2}{3}}&1&{\frac{5}{3}} \\
{\frac{1}{3}}&{\frac{2}{3}}&{\frac{4}{3}} \\
{\frac{7}{3}}&2&{\frac{2}{3}}
\end{array}} \right]$ $ – 5\left[ {\begin{array}{*{20}{l}}
{\frac{2}{5}}&{\frac{3}{5}}&1 \\
{\frac{1}{5}}&{\frac{2}{5}}&{\frac{4}{5}} \\
{\frac{7}{5}}&{\frac{6}{5}}&{\frac{2}{5}}
\end{array}} \right]$

$ = \left[ {\begin{array}{*{20}{l}}
2&3&5 \\
1&2&4 \\
7&6&2
\end{array}} \right]$ $ – \left[ {\begin{array}{*{20}{l}}
2&3&5 \\
1&2&4 \\
7&6&2
\end{array}} \right]$

$ = \left[ {\begin{array}{*{20}{l}}
0&0&0 \\
0&0&0 \\
0&0&0
\end{array}} \right]$

Standard 12

Mathematics

यदि $\left[ {\begin{array}{{20}{c}}2&{ – 3}\\4&0\end{array}} \right] – \left[ {\begin{array}{{20}{c}}a&c\\b&d\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}1&4\\2&{ – 5}\end{array}} \right]$, तो $(a,b,c,d) = $

easy

$A =\left[a_{i j}\right]_{m \times n !}$ एक वर्ग आव्यूह है यदि

easy

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

easy

इकाई का एक सम्मिश्र घनमूल $\omega$ लीजिए, जहाँ $\omega \neq 1$ तथा $P=\left[p_{i j}\right]$ एक $n \times n$ आव्यूह लीजिए, जहाँ $p_{i j}=\omega^{i+j}$ तब $P ^2 \neq 0$, जब $n =$

$(A)$ $57$ $(B)$ $55$ $(C)$ $58$ $(D)$ $56$

normal

(IIT-2013)

माना $A$ एक $2 \times 2$ का आव्यूह है जिसके लिए $\operatorname{det}( A )=-1$ तथा $\operatorname{det}(( A + I )(\operatorname{Adj}( A )+ I ))=4$ हैं। तो $A$ के विकर्ण के अवयवों का योग हो सकता है :

hard

(JEE MAIN-2022)

Solution

Similar Questions

यदि $\left[ {\begin{array}{*{20}{c}}2&{ – 3}\\4&0\end{array}} \right] – \left[ {\begin{array}{*{20}{c}}a&c\\b&d\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}1&4\\2&{ – 5}\end{array}} \right]$, तो $(a,b,c,d) = $

$A =\left[a_{i j}\right]_{m \times n !}$ एक वर्ग आव्यूह है यदि

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

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यदि $\left[ {\begin{array}{{20}{c}}2&{ – 3}\\4&0\end{array}} \right] – \left[ {\begin{array}{{20}{c}}a&c\\b&d\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}1&4\\2&{ – 5}\end{array}} \right]$, तो $(a,b,c,d) = $