Question

21. If A is a 3 x 3 matrix and det(3A) = k(det A) then k =​

Answer 1

If A is a 3 x 3 matrix,

det(3A)

It is of the form det(kA)

We have det(kA) = kⁿ det(A) where n is the order of matrix.

det(3A) = 3³|A| = 27 |A|

Therefore, k = 27

Answer 2

Given,

A = 3 x 3 Matrix

det (3A) = k

We know that,

$\qquad \bf|kA| \: = \: k^{n} |A|$

Finding value of k,

$\qquad \sf = \: k^{n} |A|$

$\: \: \: \:$ k = 3³|A|

$\: \: \: \:$k = 27|A|

Hence,

The value of k is 27

$\:$