SOLUTION: hello sir, can you tell me, how we know that which Row(column) operation should we use in the first step of determinant when we are solving it....i am asking it because you know

Algebra ->  Matrices-and-determiminant -> SOLUTION: hello sir, can you tell me, how we know that which Row(column) operation should we use in the first step of determinant when we are solving it....i am asking it because you know       Log On


   

Question 640341: hello sir, can you tell me, how we know that which Row(column) operation should we
use in the first step of determinant when we are solving it....i am asking it because you know determinant has many ways to solve.
for ex: Let A be a determinant.
|29 26 22|
A = |25 31 27|
|63 54 46|
it has many ways to solve, some give exact answer and some wrong answer.
then how we know which operation we have to apply??
kindly reply fast.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
|29 26 22|
|25 31 27|
|63 54 46|

This pattern of triple products is not hard to learn.  Observe that 
two of the 6 products are diagonals and the others are triangles. 
There are 6 products.  The first three are added and the last three subtracted:

First triple product:

|29 26 22|
|25 31 27|
|63 54 46|   1st product = 29×31×46 = 41354 (added)

Second triple product:

|29 26 22|
|25 31 27|
|63 54 46|   2nd product = 26×27×63 = 44226 (added)

Third triple product:

|29 26 22|
|25 31 27|
|63 54 46|   3rd product = 22×25×54 = 29700 (added)

Fourth triple product:

|29 26 22|
|25 31 27|
|63 54 46|   4th product = 22×31×63 = 42966 (subtracted)

Fifth triple product:

|29 26 22|
|25 31 27|
|63 54 46|   5th triple product = 26×25×46 = 29900 (subtracted)

Sixth product:

|29 26 22|
|25 31 27|
|63 54 46|   6th triple product = 29×27×54 = 42282 (subtracted)

Determinant = 1st + 2nd + 3rd - 4th - 5th - 6th =

41354 + 44226 + 29700 - 42966 - 29900 - 42282 = 132 

Answer: 132

Edwin