यदि A एक 3 times 3 कोटि का वर्ग आव्युह है तो | vedclass

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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 $C$.

यदि $A$ एक $3 \times 3$ कोटि का वर्ग आव्युह है तो $|k A |$ का मान होगा:

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