If a ne 6, b, c satisfy left| begin{array}{cc | vedclass

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

Question

(C) Given the determinant equation: $\left| \begin{array}{ccc} a & 2b & 2c \ 3 & b & c \ 4 & a & b \end{array} ight| = 0$. Applying the row operat

Vedclass · Accepted Answer

$b^3$

Vedclass · Answer

(C) Given the determinant equation: $\left| \begin{array}{ccc} a & 2b & 2c \ 3 & b & c \ 4 & a & b \end{array} ight| = 0$. Applying the row operation $R_1 	o R_1 - 2R_2$: $\left| \begin{array}{ccc} a - 6 & 2b - 2b & 2c - 2c \ 3 & b & c \ 4 & a & b \end{array} ight| = 0$ $\left| \begin{array}{ccc} a - 6 & 0 & 0 \ 3 & b & c \ 4 & a & b \end{array} ight| = 0$. Expanding along the first row: $(a - 6)(b^2 - ac) = 0$. Since $a 
e 6$,we must have $b^2 - ac = 0$,which implies $ac = b^2$. Multiplying both sides by $b$,we get $abc = b^3$.

If $a \ne 6, b, c$ satisfy $\left| \begin{array}{ccc} a & 2b & 2c \\ 3 & b & c \\ 4 & a & b \end{array} \right| = 0$,then $abc = $

Similar Questions

The planes $x = cy + bz, y = az + cx, z = bx + ay$ pass through one line,if

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

Evaluate the determinant: $\left| \begin{array}{lll} a-b & b-c & c-a \\ b-c & c-a & a-b \\ c-a & a-b & b-c \end{array} \right|$

If $A = \begin{bmatrix} 1 & 0 & 1 \\ 2 & 1 & 0 \\ 3 & 2 & 1 \end{bmatrix}$, then $\det(A)$ is equal to

The constant term of the polynomial $\left|\begin{array}{ccc}x+3 & x & x+2 \\ x & x+1 & x-1 \\ x+2 & 2x & 3x+1\end{array}\right|$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module