Question

In a third order determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms,.Then it can be decomposed into n determinants, where n has value:

• A. 1
• B. 9
• C. 16
• D. 24

Answer 1

Answer: (D)

24

We know that
If the elements of row or column of a determinant of order 3 consists of m,n,p terms respectively, then determinant can be expressed in the sum of $m\times n\times p$ determinant of same order.
Here,$n=2\times 3\times 4=24$