Show that the value of the determinant remains unchanged on interchanging the rows and columns.

Asked by Topperlearning User | 28th Apr, 2016, 01:28: PM

Expert Answer:

On interchanging the rows and columns,

 

begin mathsize 14px style triangle subscript 1 equals open vertical bar table row 1 2 3 row 5 5 6 row 7 7 8 end table close vertical bar
E x p a n d i n g space a l o n g space R subscript 1 comma
triangle subscript 1 equals 1 open vertical bar table row 5 6 row 7 8 end table close vertical bar minus 2 open vertical bar table row 5 6 row 7 8 end table close vertical bar plus 3 open vertical bar table row 5 5 row 7 8 end table close vertical bar
space space space space space space space equals 1 open parentheses 40 minus 42 close parentheses minus 2 open parentheses 40 minus 42 close parentheses
space space space space space space space equals 2
rightwards double arrow triangle equals triangle subscript 1
T h u s comma space t h e space v a l u e space o f space t h e space d e t e r m i n a n t space r e m a i n s space u n c h a n g e d space o n space i n t e r c h a n g i n g space t h e
r o w s space a n d space c o l u m n s. end style

                                                                                           

 

 

Answered by  | 28th Apr, 2016, 03:28: PM