If$\left| \begin{matrix} x^{2} + x & 3x - 1 & - x + 3 \ 2x + 1 & 2 + x^{2} & x^{3} - 3 \ x - 3 & x^{2} + 4 & 3x \end{matrix} ight|$ $= a_{0} + a_{1}x + a_{2}x^{2} +_{.}\ldots + a_{7}x^{7},$ The value of $a_{0}$is

Question

If$\left| \begin{matrix} x^{2} + x & 3x - 1 & - x + 3 \ 2x + 1 & 2 + x^{2} & x^{3} - 3 \ x - 3 & x^{2} + 4 & 3x \end{matrix} ight|$ $= a_{0} + a_{1}x + a_{2}x^{2} +_{.}\ldots + a_{7}x^{7},$ The value of $a_{0}$is

Dr. Abubacker · Accepted Answer

(d)
Putting $x = 0$ in the given determinant equation we get
$a_{0} = \left| \begin{matrix}
0 & - 1 & 3 \
1 & 2 & - 3 \
 - 3 & 4 & 0
\end{matrix} ight|$
$= 1(0 - 9) + 3(4 + 6)$
$= 30 - 9 = 21$

Q. If$\left| \begin{matrix} x^{2} + x & 3x - 1 & - x + 3 \\ 2x + 1 & 2 + x^{2} & x^{3} - 3 \\ x - 3 & x^{2} + 4 & 3x \end{matrix} \right|$ $= a_{0} + a_{1}x + a_{2}x^{2} +_{.}\ldots + a_{7}x^{7},$ The value of $a_{0}$is

Explanation

Reviewed by Dr. Abubacker

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