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**Fwahm** Prove the following:

|1 a bc| --|1 a a^2|----------------- |1 a a^2|

|1 b ac| = |1 b b^2| = (c-a)(b-a)(c-b)|0 1 b+a |=(c-a)(b-a)(c-b)

|1 c ab| --|1 c c^2|----------------- |0 0 1 |

Using only these rules:

1: If each element of a one row or column of a determinant is multiplied by a number k, the value of the determinant is multiplied by k.

2: The value of a determinant is zero if

a: all elements of one row or column are zero, or if

b: two rows or columns are identical, or if

c: two rows or columns are proportional

3: If two rows or columns of a determinant are interchanged, the value of the determinant changes sign.

4: The value of a determinant is unchanged if

a: rows are written as columns and columns as rows, or if

b: we add to each element of one row or column, k times the corresponding element of another row or column, where k is any number.