mathrm{A} એ 3 times 3 કક્ષાનો ચોરસ શ્રેણિક હો | vedclass

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

Question

$A$ is a square matrix of order $3 	imes 3$

Let $A=\left[\begin{array}{lll}a_{1} & b_{1} & c_{1} \ a_{2} & b_{2} & c_{2} \ a_{3}

Vedclass · Accepted Answer

$k^3|A|$

Vedclass · Answer

$A$ is a square matrix of order $3 	imes 3$

Let $A=\left[\begin{array}{lll}a_{1} & b_{1} & c_{1} \ a_{2} & b_{2} & c_{2} \ a_{3} & b_{3} & c_{3}\end{array}ight]$

Then, $k A=\left[\begin{array}{lll}k a_{1} & k b_{1} & k c_{1} \ k a_{2} & k b_{2} & k c_{2} \ k a_{3} & k b_{3} & k c_{3}\end{array}ight]$

$	herefore|k A|=\left|\begin{array}{lll}k a_{1} & k b_{1} & k c_{1} \ k a_{2} & k b_{2} & k c_{2} \ k a_{3} & k b_{3} & k c_{3}\end{array}ight|$

$=k^{3}\left|\begin{array}{lll}a_{1} & b_{1} & c_{1} \ a_{2} & b_{2} & c_{2} \ a_{3} & b_{3} & c_{3}\end{array}ight|$     (Taking out common factors $k$ from each row)

$=k^{3}|A|$

$	herefore|k A|=k^{3}|A|$

Hence, the correct answer is $C$.

$\mathrm{A}$ એ $3 \times 3$ કક્ષાનો ચોરસ શ્રેણિક હોય, તો $|\mathrm{k A}|$ $=$ ........

Similar Questions

$\lambda $ ની . . . . કિમત માટે સમીકરણની સંહતિ $2x - y - z = 12,$ $x - 2y + z = - 4,$ $x + y + \lambda z = 4$ ને એકપણ ઉકેલ શકય નથી.

જો રેખીય સમીકરણો $x - 4y + 7z = g,\,3y - 5z = h, \,-\,2x + 5y - 9z = k$ એ સુસંગત હોય તો . . .