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A 3x3 determinant has each entry written as a sum of terms: the first column entries are (a+p), (b+q), (c+r); the second column entries are (l+x), (m+y), (n+z); the third column entries are (u+f), (v+g), (w+h). Using the property that a determinant splits over sums in entries, into how many determinants (K) does it separate so that every entry in each is a single term?

1. 6
2. 8
3. 9
4. 12

Correct answer: 8

Solution

Each of the 3 columns is a sum of two single-term columns, so the determinant splits into 2³ = 8 determinants.

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