## Friday, November 6, 2009

### How to Calculate the Value of Determinant ?

Calculating the value of determinant is very easy  and it is very important topic in Matrix and Determinant lesson of Business Mathematics . Just understand its main steps

First see following example

```
1  2   3

। A । =        4   5   6

7   8   9

```

Above is determinant and we can calculate its value by expending it

If we calculate co-factors of first row and then multiply with respective element and then sum of these . After this what we found will be the value of determinant .

You should also know co-factor

What is co- factor ?

If we multiply - 1's power m + n with minor , then what we obtain will be co -factor .

You should also know minor

What is minor

Minor is submatrix , if we leave selected element's row and column

for example

``` ------1 2 3

। A । = 4 5 6

7 8 9

------------- 5 6
1's minor is =

8 9

```

1' co-factor = - 1's power ( 1+1 because it is first row and first column element ) and

```multiply with   5  6

--------------- 8   9
```

Now , you will able to calculate the value of determinant

```। A । = 1 X 5 6 - 2 X 4 6 + 3 X 4 5

8 9       7 9      7 8

```
। A । = 1 X ( 9 x 5 - 6 X 8 ) - 2 ( 9 X 4 - 7 X 6 ) + 3 X ( 8 X 4 - 7 X 5 )

। A । = -3 + 12 -9 = 0

So , value of determinant is Zero

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