જો $\left| {\,\begin{array}{*{20}{c}}a&b&{a + b}\\b&c&{b + c}\\{a + b}&{b + c}&0\end{array}\,} \right| = 0$; તો $a,b,c$ એ $.. . .$ શ્રેણીમાં છે .
A
સમાંતર
B
સમગુણોતર
C
સ્વરિત
D
એકપણ નહી.
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B
સમગુણોતર
Let $a,b,c$ are in $G.P.$ and assume $ a=1,b=2,c=4 $
$\therefore \,\,\,\,\,A = \left| {\,\begin{array}{*{20}{c}}1&2&3\\2&4&6\\3&6&0\end{array}\,} \right|\,\, = \,\,0$ .
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If $1,\omega ,{\omega ^2}$ are the cube roots of unity, then $\Delta = \left| {\,\begin{array}{*{20}{c}}1&{{\omega ^n}}&{{\omega ^{2n}}}\\{{\omega ^n}}&{{\omega ^{2n}}}&1\\{{\omega ^{2n}}}&1&{{\omega ^n}}\end{array}\,} \right|$ is equal to
જો $A$ એ $3 \times 3$ કક્ષાનો શ્રેણિક છે. અને $\operatorname{det}(A)=2$ .જો . ${n}=\operatorname{det}(\underbrace{\operatorname{adj}(\operatorname{adj}(\ldots . .(\operatorname{adj} A)}_{2024-\text { times }})))$ .તો $n$ ને $9$ વડે ભાગતા શેષ કેટલી મળે.
અહી $x =\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]$ અને $A =\left[\begin{array}{ccc}-1 & 2 & 3 \\ 0 & 1 & 6 \\ 0 & 0 & -1\end{array}\right]$ આપેલ છે. જો $k \in N$, if $X ^{\prime} A ^{ k } X =33$, હોય તો $k$ ની કિમંત મેળવો.