NIELIT 2017 OCT Scientific Assistant A (CS) - Section C: 9

Question

$M$ is a square matrix of order $’n’$ and its determinant value is $5.$ If all the elements of $M$ are multiple by $2,$ its determinant value becomes $40.$ The value of $’n’$ is

• A. $2$
• B. $3$
• C. $5$
• D. $4$

Answer 1

$\left | k\times A_{n\times n} \right |=k^{n}\times\left | A_{n\times n} \right |$  (Reference: Determinant when multiplying a matrix by a constant)

$\therefore$ Let the original value of determinant be  $\Delta$  i.e.  $\Delta=5$

When each element of the matrix is multiplied by $2$, the resultant determinant becomes $40$

$\therefore$  $2^{n}\times 5=40 \Rightarrow 2^{n}=8 \Rightarrow n=3$

Option B is correct.

Answer 2

Option B..

The order of matrix is 3x3 matrix.