If A=left|begin{array}{ccc}a_{1} & b_{1} & c_ | vedclass

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

Question

(B) Given the determinant $A = \left|\begin{array}{ccc}a_{1} & b_{1} & c_{1} \ a_{2} & b_{2} & c_{2} \ a_{3} & b_{3} & c_{3}\end{array}ight|$.We a

Vedclass · Accepted Answer

$A=B$

Vedclass · Answer

(B) Given the determinant $A = \left|\begin{array}{ccc}a_{1} & b_{1} & c_{1} \ a_{2} & b_{2} & c_{2} \ a_{3} & b_{3} & c_{3}\end{array}ight|$.We are given $B = \left|\begin{array}{ccc}c_{1} & c_{2} & c_{3} \ a_{1} & a_{2} & a_{3} \ b_{1} & b_{2} & b_{3}\end{array}ight|$.First,swap the first and second rows of $B$ to get $B' = -\left|\begin{array}{ccc}a_{1} & a_{2} & a_{3} \ c_{1} & c_{2} & c_{3} \ b_{1} & b_{2} & b_{3}\end{array}ight|$.Next,swap the second and third rows of $B'$ to get $B'' = -(-1) \left|\begin{array}{ccc}a_{1} & a_{2} & a_{3} \ b_{1} & b_{2} & b_{3} \ c_{1} & c_{2} & c_{3}\end{array}ight| = \left|\begin{array}{ccc}a_{1} & a_{2} & a_{3} \ b_{1} & b_{2} & b_{3} \ c_{1} & c_{2} & c_{3}\end{array}ight|$.Since the determinant of a matrix is equal to the determinant of its transpose,$\left|\begin{array}{ccc}a_{1} & a_{2} & a_{3} \ b_{1} & b_{2} & b_{3} \ c_{1} & c_{2} & c_{3}\end{array}ight| = \left|\begin{array}{ccc}a_{1} & b_{1} & c_{1} \ a_{2} & b_{2} & c_{2} \ a_{3} & b_{3} & c_{3}\end{array}ight| = A$.Therefore,$A = B$.

If $A=\left|\begin{array}{ccc}a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3}\end{array}\right|$ and $B=\left|\begin{array}{ccc}c_{1} & c_{2} & c_{3} \\ a_{1} & a_{2} & a_{3} \\ b_{1} & b_{2} & b_{3}\end{array}\right|$,then

Similar Questions

By using properties of determinants,show that:
$\left|\begin{array}{lll}1 & a & a^{2} \\ 1 & b & b^{2} \\ 1 & c & c^{2}\end{array}\right|=(a-b)(b-c)(c-a)$

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

The value of $\left| \begin{matrix} \sin \alpha & \cos \alpha & \sin(\alpha + \gamma) \\ \sin \beta & \cos \beta & \sin(\beta + \gamma) \\ \sin \delta & \cos \delta & \sin(\delta + \gamma) \end{matrix} \right|$ is

If $x, y, z$ are all positive and are the $p$-th,$q$-th,and $r$-th terms of a geometric progression respectively,then the value of the determinant $\left|\begin{array}{lll} \log x & p & 1 \\ \log y & q & 1 \\ \log z & r & 1 \end{array}\right|$ equals:

If $\left| \begin{array}{ccc} a & b & c \\ m & n & p \\ x & y & z \end{array} \right| = k$,then $\left| \begin{array}{ccc} 6a & 2b & 2c \\ 3m & n & p \\ 3x & y & z \end{array} \right| = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module