left|begin{array}{ccc}a-b-c & 2a & 2a 2b & b | vedclass

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

Question

(D) Let $\Delta = \left|\begin{array}{ccc}a-b-c & 2a & 2a \ 2b & b-c-a & 2b \ 2c & 2c & c-a-b\end{array}ight|$.Applying $R_1 ightarrow R_1 + R_2

Vedclass · Accepted Answer

$(a+b+c)^3$

Vedclass · Answer

(D) Let $\Delta = \left|\begin{array}{ccc}a-b-c & 2a & 2a \ 2b & b-c-a & 2b \ 2c & 2c & c-a-b\end{array}ight|$.Applying $R_1 ightarrow R_1 + R_2 + R_3$,we get:$\Delta = \left|\begin{array}{ccc}a+b+c & a+b+c & a+b+c \ 2b & b-c-a & 2b \ 2c & 2c & c-a-b\end{array}ight|$.Taking $(a+b+c)$ common from $R_1$:$\Delta = (a+b+c) \left|\begin{array}{ccc}1 & 1 & 1 \ 2b & b-c-a & 2b \ 2c & 2c & c-a-b\end{array}ight|$.Applying $C_2 ightarrow C_2 - C_1$ and $C_3 ightarrow C_3 - C_1$:$\Delta = (a+b+c) \left|\begin{array}{ccc}1 & 0 & 0 \ 2b & -(a+b+c) & 0 \ 2c & 0 & -(a+b+c)\end{array}ight|$.Expanding along $R_1$:$\Delta = (a+b+c) [1 \cdot (-(a+b+c)) \cdot (-(a+b+c)) - 0]$$\Delta = (a+b+c) (a+b+c)^2 = (a+b+c)^3$.

$\left|\begin{array}{ccc}a-b-c & 2a & 2a \\ 2b & b-c-a & 2b \\ 2c & 2c & c-a-b\end{array}\right|$ is equal to

Similar Questions

Phosgene is formed slowly from which one of the following on exposure to air and sunlight?

$A$ circle $C_1$ of radius $2$ touches both $x$-axis and $y$-axis. Another circle $C_2$ whose radius is greater than $2$ touches circle $C_1$ and both the axes. Then the radius of circle $C_2$ is-

Gluconeogenesis is the process of....

The absolute value of the tangent of the difference of the angles made by the lines $4x^2 - 24xy + 11y^2 = 0$ with the $X$-axis is

The maximum value of $f(x) = x^4 e^{-x^2}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module