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20 15 math 2 review book
From the basic properties of determinant: the first column of determinant plus the second column plus the third column, the value of determinant is unchanged.

∴|a 1+a2; a2+a3; a3+a 1 | = | a 1+a2+a2+a3; a2+a3; a3+a 1|

= | a 1+a2+a2+a3+a3+a 1; a2+a3; a3+a 1|

= | 2(a 1+a2+a3); a2+a3; a3+a 1|

= 2 | a 1+a2+a3; a2+a3; A3+a 1|: The common factor of a series of determinants can be

Mentioned outside the determinant