The value of left|begin{array}{lll}(a+1)(a+2) | vedclass

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

Question

(B) Let $\Delta = \left|\begin{array}{lll}(a+1)(a+2) & a+2 & 1 \ (a+2)(a+3) & a+3 & 1 \ (a+3)(a+4) & a+4 & 1\end{array}ight|$.Applying row operati

Vedclass · Accepted Answer

$-2$

Vedclass · Answer

(B) Let $\Delta = \left|\begin{array}{lll}(a+1)(a+2) & a+2 & 1 \ (a+2)(a+3) & a+3 & 1 \ (a+3)(a+4) & a+4 & 1\end{array}ight|$.Applying row operations $R_{2} ightarrow R_{2} - R_{1}$ and $R_{3} ightarrow R_{3} - R_{1}$:$\Delta = \left|\begin{array}{ccc}(a+1)(a+2) & a+2 & 1 \ (a+2)(a+3) - (a+1)(a+2) & (a+3) - (a+2) & 1 - 1 \ (a+3)(a+4) - (a+1)(a+2) & (a+4) - (a+2) & 1 - 1\end{array}ight|$$\Delta = \left|\begin{array}{ccc}(a+1)(a+2) & a+2 & 1 \ (a+2)(a+3-a-1) & 1 & 0 \ (a^2+7a+12) - (a^2+3a+2) & 2 & 0\end{array}ight|$$\Delta = \left|\begin{array}{ccc}(a+1)(a+2) & a+2 & 1 \ 2(a+2) & 1 & 0 \ 4a+10 & 2 & 0\end{array}ight|$Expanding along the third column:$\Delta = 1 	imes [2(a+2) 	imes 2 - 1 	imes (4a+10)]$$\Delta = 4(a+2) - (4a+10)$$\Delta = 4a + 8 - 4a - 10$$\Delta = -2$.

The value of $\left|\begin{array}{lll}(a+1)(a+2) & a+2 & 1 \\ (a+2)(a+3) & a+3 & 1 \\ (a+3)(a+4) & a+4 & 1\end{array}\right|$ is

Similar Questions

If $b$ and $c$ are non-zero real numbers,$A = \begin{bmatrix} 1 & b & c \\ b & 2 & 3 \\ c & 3 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} 0 & b & c \\ -b & 0 & 2 \\ -c & -2 & 0 \end{bmatrix}$,then $\det(A+B) = $

The value of $a$ for which the system of equations has a non-zero solution is
$a^{3} x+(a+1)^{3} y+(a+2)^{3} z=0$
$a x+(a+1) y+(a+2) z=0$
$x+y+z=0$

If the area of a triangle is $4$ sq. units whose vertices are $(k, 0), (4, 0)$ and $(0, 2)$,then the value of $k$ is . . . . . . .

Area of the triangle formed by points $(102, -4)$,$(105, -2)$,and $(103, -3)$ is:

Evaluate $\left|\begin{array}{ccc}\cos \alpha \cos \beta & \cos \alpha \sin \beta & -\sin \alpha \\ -\sin \beta & \cos \beta & 0 \\ \sin \alpha \cos \beta & \sin \alpha \sin \beta & \cos \alpha\end{array}\right|$

Vedclass Test Series

Exam Paper Generator

Online Exam Module