it is a determinant.

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it is a determinant.

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As we cannot evaluate the determinant by expansion, we have to reduce the determinant by row and column operations so that we can see that the determinant is zero. Two columns or rows will be identical.

The operations Column 1 - column2 and column 2 - column 3 are done.

25 21 219

15 27 198

21 17 181

row 1 - row 2 and row 2 - row 3 :

10 -6 21

-6 10 17

21 17 181

row3 - 2 * row 1, row2 + row1 and divide by 2

10 -6 21

2 2 19

1 29 139

row 3 - 4 * row 2

10 -6 21

2 2 19

-7 21 63

row 3 / 7 and row1 + row 2, then divide row 1 by 4.

3 -1 10

2 2 19

-1 3 9

Row 1 + row 3:

2 2 19

2 2 19

-1 3 9

Since two rows are equal, the determinant is 0.

The operations Column 1 - column2 and column 2 - column 3 are done.

25 21 219

15 27 198

21 17 181

row 1 - row 2 and row 2 - row 3 :

10 -6 21

-6 10 17

21 17 181

row3 - 2 * row 1, row2 + row1 and divide by 2

10 -6 21

2 2 19

1 29 139

row 3 - 4 * row 2

10 -6 21

2 2 19

-7 21 63

row 3 / 7 and row1 + row 2, then divide row 1 by 4.

3 -1 10

2 2 19

-1 3 9

Row 1 + row 3:

2 2 19

2 2 19

-1 3 9

Since two rows are equal, the determinant is 0.