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

If each element of a determinant of third order with value $A$ is multiplied by $3$,then the value of the newly formed determinant is: (in $A$)

Let $A = \begin{bmatrix} 1 + x^2 - y^2 - z^2 & 2(xy + z) & 2(zx - y) \\ 2(xy - z) & 1 + y^2 - z^2 - x^2 & 2(yz + x) \\ 2(zx + y) & 2(yz - x) & 1 + z^2 - x^2 - y^2 \end{bmatrix}$. Then $\det(A)$ is equal to:

If $a_{n} (>0)$ is the $n^{\text{th}}$ term of a $G$.$P$.,then the value of the determinant $\left|\begin{array}{lll}\log a_{n} & \log a_{n+1} & \log a_{n+2} \\ \log a_{n+3} & \log a_{n+4} & \log a_{n+5} \\ \log a_{n+6} & \log a_{n+7} & \log a_{n+8}\end{array}\right|$ is equal to:

$\left|\begin{array}{ccc}1 & 1 & 1 \\ a^2 & b^2 & c^2 \\ a^3 & b^3 & c^3\end{array}\right|=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module