If left| begin{array}{ccc} a & b & c m & n & | vedclass

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

Question

(D) Given that $\left| \begin{array}{ccc} a & b & c \ m & n & p \ x & y & z \end{array} ight| = k$.We need to evaluate $\Delta = \left| \begin{arr

Vedclass · Accepted Answer

$6k$

Vedclass · Answer

(D) Given that $\left| \begin{array}{ccc} a & b & c \ m & n & p \ x & y & z \end{array} ight| = k$.We need to evaluate $\Delta = \left| \begin{array}{ccc} 6a & 2b & 2c \ 3m & n & p \ 3x & y & z \end{array} ight|$.Taking out common factors from the rows and columns:From the first row,we can factor out $2$: $\Delta = 2 \left| \begin{array}{ccc} 3a & b & c \ 3m & n & p \ 3x & y & z \end{array} ight|$.From the first column,we can factor out $3$: $\Delta = 2 	imes 3 \left| \begin{array}{ccc} a & b & c \ m & n & p \ x & y & z \end{array} ight|$.Substituting the given value $k$: $\Delta = 6 	imes k = 6k$.

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| = $

Similar Questions

If $\Delta=\left|\begin{array}{lll}1 & a & a^2 \\ 1 & b & b^2 \\ 1 & c & c^2\end{array}\right|$ and $\Delta_1=\left|\begin{array}{ccc}1 & 1 & 1 \\ b c & c a & a b \\ a & b & c\end{array}\right|$,then

By using properties of determinants,show that:
$\left|\begin{array}{ccc}x+y+2z & x & y \\ z & y+z+2x & y \\ z & x & z+x+2y\end{array}\right|=2(x+y+z)^{3}$

The product of a matrix and its transpose is an identity matrix. The value of the determinant of this matrix is:

$\left| {\begin{array}{*{20}{c}}{a - 1}&a&{bc}\\{b - 1}&b&{ca}\\{c - 1}&c&{ab}\end{array}} \right| = $

If $A$ is a square matrix of order $3$,then which of the following statements is true? (where $I$ is the identity matrix)

Vedclass Test Series

Exam Paper Generator

Online Exam Module