$\mathrm{D}=\left|\begin{array}{ccc}\mathrm{bc} & \mathrm{ca} & \mathrm{ab} \\ \mathrm{a} & \mathrm{b} & \mathrm{c} \\ \mathrm{a}^{2} & \mathrm{~b}^{2} & \mathrm{c}^{2}\end{array}\right|$ একটি তৃতীয় মাত্রার নির্ণায়ক।

$\ \mathrm{~A}=\left[\begin{array}{rrr}1 & 3 & 2 \\ 2 & 0 & 3 \\ 1 & -1 & 1\end{array}\right]$ এবং $\mathrm{f}(\mathrm{x})=3 \mathrm{x}^{2}+2 \mathrm{x}-5$ এবং $C=\left[\begin{array}{ccc}\frac{a-b-c}{2} & a & a \\ b & \frac{b-c-a}{2} & b \\ c & c & \frac{c-a-b}{2}\end{array}\right]$

দৃশ্যকল্প: $A=\left[\begin{array}{ccc}1+x^{2}-y^{2} & 2 x y & -2 y \\ 2 x y & 1-x^{2}+y^{2} & 2 x \\ 2 y & -2 x & 1-x^{2}-y^{2}\end{array}\right]$

$\mathrm{F}(\mathrm{x})=2 \mathrm{x}^{2}-3$ এবং $\mathrm{P}=\left[\begin{array}{lll}(\mathrm{b}+\mathrm{c})^{2} & \mathrm{a}^{2} & \mathrm{bc} \\ (\mathrm{c}+\mathrm{a})^{2} & \mathrm{~b}^{2} & \mathrm{ca} \\ (\mathrm{a}+\mathrm{b})^{2} & \mathrm{c}^{2} & a b\end{array}\right]$

$\begin{array}{l}\text { দৃশ্যকল্প-১: } \mathrm{f}(\mathrm{x})=3 \mathrm{x}^{2}+5 \mathrm{x} \\ \text { দৃশ্যকল্প-২: } \mathrm{B}=\left[\begin{array}{ccc}\ell & \mathrm{m} & \mathrm{n} \\ \ell^{2} & \mathrm{~m}^{2} & \mathrm{n}^{2} \\ \ell^{3}-1 & \mathrm{~m}^{3}-1 & \mathrm{n}^{3}-1\end{array}\right]\end{array}$