left| {,begin{array}{*{20}{c}}a&b&cb& | vedclass

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

Question

(b) $\left| {\,\begin{array}{*{20}{c}}a&b&c\b&c&a\c&a&b\end{array}\,} ight| = \left| {\,\begin{array}{*{20}{c}}{a + b + c}

Vedclass · Accepted Answer

$3abc - {a^3} - {b^3} - {c^3}$

Vedclass · Answer

(b) $\left| {\,\begin{array}{*{20}{c}}a&b&c\b&c&a\c&a&b\end{array}\,} ight| = \left| {\,\begin{array}{*{20}{c}}{a + b + c}&{a + b + c}&{a + b + c}\b&c&a\c&a&b\end{array}\,} ight|$,

                                                                $({R_1} 	o {R_1} + {R_2} + {R_3})$

=$(a + b + c)$ $\left| {\,\begin{array}{*{20}{c}}{1}&{1}&{1}\b&c&a\c&a&b\end{array}\,} ight|$  =$(a + b + c)$  $\left| {\,\begin{array}{*{20}{c}}   1&1&1 \    b&c&a \    c&a&b  \end{array}\,} ight|$  = $ (a + b + c)$    $\left| {\,\begin{array}{*{20}{c}}   1&0&0 \    b&{b - c}&{c - a} \    c&{c - a}&{a - b}  \end{array}\,} ight|$

= $3abc - {a^3} - {b^3} - {c^3}$,                (After simplification).

$\left| {\,\begin{array}{*{20}{c}}a&b&c\\b&c&a\\c&a&b\end{array}\,} \right| = $

Similar Questions

સમીકરણ $\left| {\,\begin{array}{*{20}{c}}a&a&x\\m&m&m\\b&x&b\end{array}\,} \right| = 0$ ના બીજ મેળવો.

જો $\left| {\,\begin{array}{*{20}{c}}a&b&{a\alpha - b}\\b&c&{b\alpha - c}\\2&1&0\end{array}\,} \right| = 0$ અને $\alpha \ne \frac{1}{2} $ તો . . .

સમીકરણની સંહતિ $x + 4y - z = 0,$ $3x - 4y - z = 0,\,x - 3y + z = 0$ ના ઉકેલની સંખ્યા મેળવો.

જો સમીકરણ સંહિતા

$x-2 y+3 z=9$

$2 x+y+z=b$

$x-7 y+a z=24$

ને અનંત ઉકેલો હોય તો $a - b$ ની કિમત મેળવો

$x$ નું મૂલ્ય શોધો : $\left|\begin{array}{ll}2 & 3 \\ 4 & 5\end{array}\right|=\left|\begin{array}{ll}x & 3 \\ 2 x & 5\end{array}\right|$