What is the value of left|begin{array}{ccc}a | vedclass

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

Question

(B) Let $\Delta = \begin{vmatrix} a & b & c \ a-b & b-c & c-a \ b+c & c+a & a+b \end{vmatrix}$Applying $R_2 	o R_2 - R_1$:$\Delta = \begin{vmatrix}

Vedclass · Accepted Answer

$a^3+b^3+c^3-3abc$

Vedclass · Answer

(B) Let $\Delta = \begin{vmatrix} a & b & c \ a-b & b-c & c-a \ b+c & c+a & a+b \end{vmatrix}$Applying $R_2 	o R_2 - R_1$:$\Delta = \begin{vmatrix} a & b & c \ -b & -c & -a \ b+c & c+a & a+b \end{vmatrix}$Applying $R_3 	o R_3 + R_2$:$\Delta = \begin{vmatrix} a & b & c \ -b & -c & -a \ c & a & b \end{vmatrix}$Wait,let us re-evaluate the operation $R_3 	o R_3 + R_2$:$R_3$ becomes $(b+c-b, c+a-c, a+b-a) = (c, a, b)$.So,$\Delta = \begin{vmatrix} a & b & c \ -b & -c & -a \ c & a & b \end{vmatrix}$Expanding along $R_1$:$\Delta = a(-bc - (-a^2)) - b(-b^2 - (-ac)) + c(-ab - (-c^2))$$\Delta = a(a^2 - bc) - b(ac - b^2) + c(c^2 - ab)$$\Delta = a^3 - abc - abc + b^3 + c^3 - abc$$\Delta = a^3 + b^3 + c^3 - 3abc$

What is the value of $\left|\begin{array}{ccc}a & b & c \\ a-b & b-c & c-a \\ b+c & c+a & a+b\end{array}\right|=$ ?

Similar Questions

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

The area of a triangle with vertices $(-3, 0)$, $(3, 0)$, and $(0, k)$ is $9$ sq units. Find the possible values of $k$.

Evaluate the determinant: $\left|\begin{array}{ll}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right|$

The area of a triangle whose vertices are $(2, -6)$,$(5, 4)$,and $(k, 4)$ is $35$ sq. units. Then,the value of $k$ is . . . . . . .

If $\Delta=\left|\begin{array}{ccc}x-2 & 2 x-3 & 3 x-4 \\ 2 x-3 & 3 x-4 & 4 x-5 \\ 3 x-5 & 5 x-8 & 10 x-17\end{array}\right|=Ax^{3}+Bx^{2}+Cx+D$,then $B+C$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module