શ્રેણિક — ગણિત ધોરણ 12 સાયન્સ — Question

$A=\left[\begin{matrix} 5a & -b &\\ 3 & 2 \end{matrix}\right]$

$A\cdot adj\ A=A\cdot A^T$

$\therefore\left[\begin{matrix} 5a & -b &\\ 3 & 2 \end{matrix}\right]\left[\begin{matrix} 2 & b &\\ -3 & 5a \end{matrix}\right] =\left[\begin{matrix} 5a & -b &\\ 3 & 2 \end{matrix}\right]\left[\begin{matrix} 5a & 3 &\\ -b & 2 \end{matrix}\right]$

$\therefore\left[\begin{matrix} 10a+3b & 5ab-5ab &\\ 6-6 & 3b+10a \end{matrix}\right]=\left[\begin{matrix} 25a^2+b^2 & 15a-2b &\\15a-2b & 9+4 \end{matrix}\right]$

$10a+3b=15$ અને $15a-2b=0$ બંને સમીકરણ ઉકેલતા

$a=\frac{2}{5},b=3$

$\therefore 5a+b=2+3=5.$