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Question

Find $$a$$ if  $$\begin{vmatrix} i & -2i & -1\\ 3i & i^{3} & -2\\ 1& -3 & -i\end{vmatrix}$$ = $$ai$$, where $$i =\sqrt{-1}$$


Solution

Given that
$$\begin{vmatrix} i & -2i & -1\\ 3i & i^{3} & -2\\ 1& -3 & -i\end{vmatrix}=ai$$

Expanding given Determinant 
$$i(-i^4-6)+2i(-3i^2+2)-1(-9i-i^3)$$

$$=-i^5-6i-6i^3+4i+9i+i^3$$

$$=-i-6i+6i+4i+9i-i$$

$$=11i$$

Henece value of $$a=11$$

Mathematics

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