left|begin{array}{ccc}x & 3x+2 & 2x-1 2x-1 & | vedclass

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

Question

(D) Given the determinant: $\Delta = \left|\begin{array}{ccc}x & 3x+2 & 2x-1 \ 2x-1 & 4x & 3x+1 \ 7x-2 & 17x+6 & 12x-1\end{array}ight| = 0$.Apply

Vedclass · Accepted Answer

infinitely many values of $x$

Vedclass · Answer

(D) Given the determinant: $\Delta = \left|\begin{array}{ccc}x & 3x+2 & 2x-1 \ 2x-1 & 4x & 3x+1 \ 7x-2 & 17x+6 & 12x-1\end{array}ight| = 0$.Apply the row operation $R_{3} ightarrow R_{3} - 3R_{1} - 2R_{2}$:For the third row elements:$R_{3,1} = (7x-2) - 3(x) - 2(2x-1) = 7x - 2 - 3x - 4x + 2 = 0$.$R_{3,2} = (17x+6) - 3(3x+2) - 2(4x) = 17x + 6 - 9x - 6 - 8x = 0$.$R_{3,3} = (12x-1) - 3(2x-1) - 2(3x+1) = 12x - 1 - 6x + 3 - 6x - 2 = 0$.Since all elements of the third row are $0$, the value of the determinant is $0$ for all values of $x$.Therefore, the equation is true for infinitely many values of $x$.

$\left|\begin{array}{ccc}x & 3x+2 & 2x-1 \\ 2x-1 & 4x & 3x+1 \\ 7x-2 & 17x+6 & 12x-1\end{array}\right|=0$ is true for

Similar Questions

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 $a, b, c$ are non-zero real numbers and if the equations $(a-1) x=y+z, (b-1) y=z+x, (c-1) z=x+y$ have a non-trivial solution,then $ab+bc+ca=$

If $a, b, c$ are real numbers such that $a-b=1$ and $b-c=3$, then the number of matrices of the form $A=\begin{bmatrix} 1 & 1 & 1 \\ a & b & c \\ a^2 & b^2 & c^2 \end{bmatrix}$ such that $|A|=-12$ is:

If $P, Q$ and $R$ are angles of $\Delta PQR$, then the value of $\left|\begin{array}{ccc}-1 & \cos R & \cos Q \\ \cos R & -1 & \cos P \\ \cos Q & \cos P & -1\end{array}\right|$ is equal to

If $\Delta_k=\left|\begin{array}{ccc}1 & 0 & 0 \\ 0 & k & k-1 \\ 0 & k-1 & k\end{array}\right|$,then $\Delta_1+\Delta_2+\ldots+\Delta_{20}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module