જો A = left[ {begin{array}{*{20}{c}}1&2&31&4&91&8&{27}end{array}} right], તો |adj,,A|= . .. .

Q: જો $A = \left[ {\begin{array}{*{20}{c}}1&2&3\\1&4&9\\1&8&{27}\end{array}} \right]$, તો $|adj\,\,A|= . .. .$

c (c) $A = \left[ {\,\begin{array}{*{20}{c}}1&2&3\\1&4&9\\1&8&{27}\end{array}\,} \right]$ Let $c_{ij}$ be co-factor of $a_{ij}$ in $A$ Then co-factor of elements of $A $ are given by ${C_{11}} = \left| {\,\begin{array}{*{20}{c}}4&9\\18&{27}\end{array}\,} \right|\, = 36,\,{C_{21}} = \left| {\,\begin{array}{*{20}{c}}2&3\\8&{27}\end{array}\,} \right| = - 30,$$\,{C_{31}} = \left| {\,\begin{array}{*{20}{c}}2&3\\4&9\end{array}\,} \right| = 6$ ${C_{12}} = \left| {\,\begin{array}{*{20}{c}}1&9\\1&{27}\end{array}\,} \right|\, = 8,\,{C_{22}} = \left| {\,\begin{array}{*{20}{c}}1&3\\1&{27}\end{array}\,} \right| = 24,$$\,{C_{32}} = \left| {\,\begin{array}{*{20}{c}}1&3\\4&9\end{array}\,} \right| = -6$ $\,{C_{33}} = \left| {\,\begin{array}{*{20}{c}}1&2\\1&4 \end{array}\,} \right| = 2$ ==> $Adj(A)\,\, = \left| {\,\begin{array}{*{20}{c}} {36}&{ - 30}&6\\ { - 18}&{24}&{ - 6}\\ 1&{ - 6}&2 \end{array}\,} \right|\,$ ==>$Adj(A) = 36(48 - 36) + 30( - 36 + 24) + 6(108 - 96)$ ==> $Adj(A) = 144$

MCQ

ગુજરાતી માધ્યમ

જો $A = \left[ {\begin{array}{*{20}{c}}1&2&3\\1&4&9\\1&8&{27}\end{array}} \right]$, તો $|adj\,\,A|= . .. .$

A$36$
B$72$
C$144$
D
એકપણ નહી.

Easy

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

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