શ્રેણિક left[ {begin{array}{*{20}{c}}0&1&21&2&33&1&1end{array}} right], નો વ્યસ્ત મેળવો.

Q: શ્રેણિક $\left[ {\begin{array}{*{20}{c}}0&1&2\\1&2&3\\3&1&1\end{array}} \right],$ નો વ્યસ્ત મેળવો.

${A^{ - 1}} = \frac{{\text{adj}\,(A)}}{{|A|}} = \frac{1}{{|A|}}.\,\text{adj}\ (A)$ $A = \left[ {\begin{array}{*{20}{c}} 0&1&2 \\ 1&2&3 \\ 3&1&1\end{array}} \right];$ $|A| = 0-1(1-9)+2(1-6)=8-10$ $|A|= -2 \ne 0$ $\text{Adj}\ A = \left[ {\begin{array}{*{20}{c}}{{A_{11}}}&{{A_{21}}}&{{A_{31}}}\\{{A_{12}}}&{{A_{22}}}&{{A_{32}}}\\{{A_{13}}}&{{A_{23}}}&{{A_{33}}}\end{array}} \right]$ ${A_{11}} = {( - 1)^{1 + 1}}[(2)\,(1) - (3)(1)] = - 1$ ${A_{12}} = 8, \frac{1}{{1 - a}} - 1 + \frac{1}{{1 - b}} + \frac{1}{{1 - c}} = 0$, ${A_{21}} = 1, {A_{22}} = - 6$ ${A_{23}} = 3,{A_{31}} = - 1, {A_{32}} = 2, {A_{33}} = - 1$ $\therefore {A^{ - 1}} = \frac{1}{{ - 2}}\,\left[ {\begin{array}{*{20}{c}}{ - 1}&1&{ - 1}\\8&{ - 6}&2\\{ - 5}&3&{ - 1}\end{array}} \right]$ $ = \left[ {\begin{array}{*{20}{c}}{1/2}&{ - 1/2}&{1/2}\\{ - 4}&3&{ - 1}\\{5/2}&{ - 3/2}&{1/2}\end{array}} \right]$.

MCQ

ગુજરાતી માધ્યમ

શ્રેણિક $\left[ {\begin{array}{*{20}{c}}0&1&2\\1&2&3\\3&1&1\end{array}} \right],$ નો વ્યસ્ત મેળવો.

A$\left[ {\begin{array}{*{20}{c}}{\frac{1}{2}}&{ - \frac{1}{2}}&{\frac{1}{2}}\\{ - 4}&3&{ - 1}\\{\frac{5}{2}}&{\frac{{ - 3}}{2}}&{\frac{1}{2}}\end{array}} \right]$
B$\left[ {\begin{array}{*{20}{c}}{\frac{1}{2}}&{ - 4}&{\frac{5}{2}}\\1&{ - 6}&3\\1&2&{ - 1}\end{array}} \right]$
C$\frac{1}{2}\left[ {\begin{array}{*{20}{c}}1&2&3\\3&2&1\\4&2&3\end{array}} \right]$
D$\frac{1}{2}\left[ {\begin{array}{*{20}{c}}1&{ - 1}&{ - 1}\\{ - 8}&6&{ - 2}\\5&{ - 3}&1\end{array}} \right]$

Medium

ધોરણ 12 સાયન્સ
ગણિત
3 and 4 . determinant and metrices
JEE

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