The determinant left| begin{array}{ccc} 1 & 1 | vedclass

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

Question

(A) Let $D = \left| \begin{array}{ccc} 1 & 1 & 1 \ 1 & 2 & 3 \ 1 & 3 & 6 \end{array} ight|$.Applying $C_1 	o C_1 + C_2$,we get $D = \left| \begin

Vedclass · Accepted Answer

$\left| \begin{array}{ccc} 2 & 1 & 1 \ 2 & 2 & 3 \ 2 & 3 & 6 \end{array} ight|$

Vedclass · Answer

(A) Let $D = \left| \begin{array}{ccc} 1 & 1 & 1 \ 1 & 2 & 3 \ 1 & 3 & 6 \end{array} ight|$.Applying $C_1 	o C_1 + C_2$,we get $D = \left| \begin{array}{ccc} 2 & 1 & 1 \ 3 & 2 & 3 \ 4 & 3 & 6 \end{array} ight|$,which is option $B$.Applying $C_2 	o C_2 + C_3$ to the original determinant,we get $D = \left| \begin{array}{ccc} 1 & 2 & 1 \ 1 & 5 & 3 \ 1 & 9 & 6 \end{array} ight|$,which is option $C$.Applying $C_1 	o C_1 + C_2 + C_3$ to the original determinant,we get $D = \left| \begin{array}{ccc} 3 & 1 & 1 \ 6 & 2 & 3 \ 10 & 3 & 6 \end{array} ight|$,which is option $D$.Option $A$ is $\left| \begin{array}{ccc} 2 & 1 & 1 \ 2 & 2 & 3 \ 2 & 3 & 6 \end{array} ight| = 2 \left| \begin{array}{ccc} 1 & 1 & 1 \ 1 & 2 & 3 \ 1 & 3 & 6 \end{array} ight| = 2D 
eq D$.Thus,the determinant is not equal to option $A$.

The determinant $\left| \begin{array}{ccc} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & 6 \end{array} \right|$ is not equal to

Similar Questions

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

If $a, b, c$ are positive integers,then the determinant $\Delta = \begin{vmatrix} a^2 + x & ab & ac \\ ab & b^2 + x & bc \\ ac & bc & c^2 + x \end{vmatrix}$ is divisible by

If $\left| \begin{matrix} a - b - c & 2a & 2a \\ 2b & b - c - a & 2b \\ 2c & 2c & c - a - b \end{matrix} \right| = (a + b + c)(x + a + b + c)^2$,$x \ne 0$ and $a + b + c \ne 0$,then $x$ is equal to

The determinant $\left|\begin{array}{ccc}a^{2}+10 & a b & a c \\ a b & b^{2}+10 & b c \\ a c & b c & c^{2}+10\end{array}\right|$ is

If $k \in R$ and $\operatorname{det} A = \begin{vmatrix} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end{vmatrix} = K$,then $\operatorname{det} B = \begin{vmatrix} a_1 & b_1 & c_1 \\ a_2 + 2a_1 & b_2 + 2b_1 & c_2 + 2c_1 \\ a_3 & b_3 & c_3 \end{vmatrix}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module