If P, Q and R are 3 times 3 matrices such tha | vedclass

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(B) Given the matrix equation: $\begin{bmatrix} 3x^2+x+3 & 2x^2-x+4 & 7x^2+8x+5 \ 5x^2+3x+2 & 4x^2-2x-1 & 7x^2+5x+8 \ 3x^2+2x+5 & 4x^2-x-2 & 3x^2+8x

Vedclass · Accepted Answer

$136$

Vedclass · Answer

(B) Given the matrix equation: $\begin{bmatrix} 3x^2+x+3 & 2x^2-x+4 & 7x^2+8x+5 \ 5x^2+3x+2 & 4x^2-2x-1 & 7x^2+5x+8 \ 3x^2+2x+5 & 4x^2-x-2 & 3x^2+8x+7 \end{bmatrix} = Px^2+Qx+R$. To find the matrix $R$,we set $x=0$ in the given expression: $R = \begin{bmatrix} 3(0)^2+0+3 & 2(0)^2-0+4 & 7(0)^2+8(0)+5 \ 5(0)^2+3(0)+2 & 4(0)^2-2(0)-1 & 7(0)^2+5(0)+8 \ 3(0)^2+2(0)+5 & 4(0)^2-0-2 & 3(0)^2+8(0)+7 \end{bmatrix} = \begin{bmatrix} 3 & 4 & 5 \ 2 & -1 & 8 \ 5 & -2 & 7 \end{bmatrix}$. Now,we calculate the determinant of $R$: $\det R = 3((-1)(7) - (8)(-2)) - 4((2)(7) - (8)(5)) + 5((2)(-2) - (-1)(5))$ $\det R = 3(-7 + 16) - 4(14 - 40) + 5(-4 + 5)$ $\det R = 3(9) - 4(-26) + 5(1)$ $\det R = 27 + 104 + 5 = 136$.

If $P, Q$ and $R$ are $3 \times 3$ matrices such that $\begin{bmatrix} 3x^2+x+3 & 2x^2-x+4 & 7x^2+8x+5 \\ 5x^2+3x+2 & 4x^2-2x-1 & 7x^2+5x+8 \\ 3x^2+2x+5 & 4x^2-x-2 & 3x^2+8x+7 \end{bmatrix} = Px^2+Qx+R$,then $\det R = $

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