Page 131 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

Note that we may choose any row or any column.

EXAMPLE 3 Cofactor Expansion Along the First Column

Let be the matrix in Example 2. Evaluate by cofactor expansion along the first column of .

Solution

From 4

This agrees with the result obtained in Example 2.

Remark In this example we had to compute three cofactors, but in Example 2 we only had to compute two of them, since
the third was multiplied by zero. In general, the best strategy for evaluating a determinant by cofactor expansion is to expand
along a row or column having the largest number of zeros.

EXAMPLE 4 Smart Choice of Row or Column
If is the matrix

then to find it will be easiest to use cofactor expansion along the second column, since it has the most zeros:

For the determinant, it will be easiest to use cofactor expansion along its second column, since it has the most zeros:

We would have found the same answer if we had used any other row or column.