જો ત્રણ વાસ્તવિક સંખ્યાઓ $p, q, r$ એ શ્રેણિક સમીકરણ $[p\,q\,r]\,\left[ {\begin{array}{*{20}{c}}
3&4&1\\
3&2&3\\
2&0&2
\end{array}} \right] = [3\,\,\,0\,\,\,1]$ નું પાલન કરે છે તો $2p + q - r$ મેળવો.
3&4&1\\
3&2&3\\
2&0&2
\end{array}} \right] = [3\,\,\,0\,\,\,1]$ નું પાલન કરે છે તો $2p + q - r$ મેળવો.
JEE MAIN 2013, Difficult
Download our app for free and get started
Given
$\left[ {\begin{array}{*{20}{c}}
p&q&r
\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
3&4&1\\
3&2&3\\
2&0&2
\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
3&0&1
\end{array}} \right]$
$ \Rightarrow \left[ {\begin{array}{*{20}{c}}
{3p + 3q + 2r}&{4p + 2q}&{p + 3q + 2r}
\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
3&0&1
\end{array}} \right]$
$ \Rightarrow 3p + 3q + 2r = 3\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,....\left( i \right)$
$4p + 2q = 0 \Rightarrow q = - 2p\,\,\,\,\,\,\,\,......\left( {ii} \right)$
$p + 3q + 2r = 1\,\,\,\,\,\,\,\,\,\,.......\left( {iii} \right)$
On solving $(i),(ii)$ and $(iii)$ , we get
$p=1,q=-2,r=3$
$\therefore 2p + q + r = 2\left( 1 \right) + \left( { - 2} \right) - \left( 3 \right) = - 3$.
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1$\left| {\,\begin{array}{*{20}{c}}1&5&\pi \\{{{\log }_e}e}&5&{\sqrt 5 }\\{{{\log }_{10}}10}&5&e\end{array}\,} \right| = $View Solution
- 2શ્રેણિકView Solution
$A = \left[ {\begin{array}{*{20}{c}}
{{{10}^{30}} + 5}&{{{10}^{20}} + 4}&{{{10}^{20}} + 6}\\
{{{10}^4} + 2}&{{{10}^8} + 7}&{{{10}^{10}} + 2n}\\
{{{10}^4} + 8}&{{{10}^6} + 4}&{{{10}^{15}} + 9}
\end{array}} \right]$ , $n \in N$, હોય તો . .. - 3જે $\mathrm{A}=\left[\begin{array}{cc}\sqrt{2} & 1 \\ -1 & \sqrt{2}\end{array}\right], \mathrm{B}=\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right], \mathrm{C}=\mathrm{ABA}^{\mathrm{T}}$ અને $\mathrm{X}=\mathrm{A}^{\mathrm{T}} \mathrm{C}^2 \mathrm{~A}$ હોય, તો $\operatorname{det} \mathrm{X}=$________________View Solution
- 4જો $\mathrm{a, b, c}$ સમાંતર શ્રેણીમાં હોય, તો નિશ્ચાયક $\left|\begin{array}{lll}x+2 & x+3 & x+2 a \\ x+3 & x+4 & x+2 b \\ x+4 & x+5 & x+2 c\end{array}\right|$View Solution
- 5જો $A = \left[ {\begin{array}{*{20}{c}}{ - 1}&2\\2&{ - 1}\end{array}} \right]$ અને $B = \left[ \begin{array}{l}3\\1\end{array} \right],AX = B$, તો $X = $View Solution
- 6$\left[ {x\,y\,z} \right]\,\left[ {\begin{array}{*{20}{c}}View Solution
a&h&g\\
h&b&f\\
g&f&c
\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}
x\\
y\\
z
\end{array}} \right]$ ની કક્ષા મેળવો. - 7ધારો કે $A$ એ એવો $n \times n$ શ્રેણિક છે કે જેથી $| A |=2$ પર થાય.જો શ્રેણિક $\operatorname{Adj}\left(2 \cdot \operatorname{Adj}\left(2 A ^{-1}\right)\right) \cdot$ નો નિશ્ચાયક $2^{84}$ હોય, તો $n =.............$.View Solution
- 8$\left| {\,\begin{array}{*{20}{c}}{a - 1}&a&{bc}\\{b - 1}&b&{ca}\\{c - 1}&c&{ab}\end{array}\,} \right| = $View Solution
- 9જો $A = \left| {\,\begin{array}{*{20}{c}}1&1&1\\a&b&c\\{{a^3}}&{{b^3}}&{{c^3}}\end{array}\,} \right|,B = \left| {\,\begin{array}{*{20}{c}}1&1&1\\{{a^2}}&{{b^2}}&{{c^2}}\\{{a^3}}&{{b^3}}&{{c^3}}\end{array}\,} \right|,C = \left| {\,\begin{array}{*{20}{c}}a&b&c\\{{a^2}}&{{b^2}}&{{c^2}}\\{{a^3}}&{{b^3}}&{{c^3}}\end{array}\,} \right|,$ તો આપલે પૈકી ક્યો સંબંધ સાચો છે .View Solution
- 10$\left| {\begin{array}{*{20}{c}}View Solution
{4 + {x^2}}&{ - 6}&{ - 2}\\
{ - 6}&{9 + {x^2}}&3\\
{ - 2}&3&{1 + {x^2}}
\end{array}} \right|$ $;(x\neq0)$ એ . . . વડે વિભાજ્ય નથી .