Determinant question

Question

If det= |a b c|

          | d e f|  =  4

           |g h i|

 

 

then det= | a-9g   3b-27h   c-9i |

               |  d       3e         f |            =?

               |  g      3h         i |

 

 

i can't solve this kind of determinant questions.

Answer 1

First, multiply the second column of the original matrix by 3 (this operation multiplies the original determinant by 3)

 

Then, add -9 times row 3 to row 1 (adding a multiple of a row to another row does not change the value of the determinant)

 

So, the answer is 4(3) = 12