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Let |{:(x,2,x),(x^(2),x,6),(x,x,6):}|=Ax...

Let `|{:(x,2,x),(x^(2),x,6),(x,x,6):}|=Ax^(4)+Bx^(3)+Cx^(2)+Dx+E` the value of 5A+4B+3C+2D+E is equal to

A

-16

B

-11

C

0

D

16

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The correct Answer is:
To solve the determinant problem step by step, we will calculate the determinant of the given matrix and then compare it with the polynomial form to find the coefficients A, B, C, D, and E. ### Step 1: Write the Determinant We start with the determinant of the matrix: \[ \begin{vmatrix} x & 2 & x \\ x^2 & x & 6 \\ x & x & 6 \end{vmatrix} \]
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