Question

If A is a 3x3 matrix[A]≠0 [3A]=[KA]
Then find the value of K

Answer 1

Given:

If A is a 3x3 matrix such that [A]≠0  |3A| = k |A|.

To find:

Then find the value of K.

Solution:

Since, here, it is given that-

A is a $3\times 3$ matrix ,  A has 3 rows and 3 columns.

therefore, 3A is the matrix obtained when we multiply each entry of A by 3.

thus, if A has row vectors, $x_{1},x_{2}$  and  $x_{3}$.

⇒ 3A has row vectors $3x_{1} ,3x_{2}$  and  $3x_{3}$.

Also, we know that multiplying a single row of a matrix A by a scalar R has the  effect of multiplying the determinant of A by R, we get;

$det (3A) =$

$3\times 3\times 3 det(A)\\\\=27 det(A)$

therefore, in |3A|=k |A|

⇒ k = 27.