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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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 = $

Similar Questions

If $x^{3}-2x^{2}-9x+18=0$ and $A=\left|\begin{array}{lll}1 & 2 & 3 \\ 4 & x & 6 \\ 7 & 8 & 9\end{array}\right|$,then the maximum value of $A$ is

The value of the determinant $\left| \begin{array}{ccc} 1 & 2 & 3 \\ 3 & 5 & 7 \\ 8 & 14 & 20 \end{array} \right|$ is

Find the equation of the line joining $(3, 1)$ and $(9, 3)$ using determinants.

If $a, b, c$ are sides of a scalene triangle,then the value of $\left| \begin{array}{ccc} a & b & c \\ b & c & a \\ c & a & b \end{array} \right|$ is

$A$ root of the equation $\left| \begin{array}{ccc} 3 - x & -6 & 3 \\ -6 & 3 - x & 3 \\ 3 & 3 & -6 - x \end{array} \right| = 0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module