In Example 2, change the −2 in the first row to 0 and then find the determinant.

Data from Example 2

In evaluating the following determinant, note that the third column has two zeros. This means that expanding by the third column will require less numerical work. Therefore,

As we noted in Chapter 5, most calculators can be used to quickly evaluate determinants. Figure 16.20 shows the calculator evaluation of this determinant.

3-2 0 2 1 0-1 4 2-2 0-1 -3 1 2 -1 20 1 = +(0) -3 = 0 1-2 2 -1 -1 = 3 (-1) -3 2 3-2 2 3-2 2 -3 1-2 +2 1 0 4 21-1 2 -1 -1 -2 1-2 + (2) -1 3-2 2 1 0 4 2 -1 -1 3-2 2 0 4 1 -3 1-2 3 + + + -1 -1 -1 1-2 2-1 2-1 4 expanding first determinant by first column expanding second determinant by second column = [3(-1-2) + 3(2+ 2) + 2(4-2)] + 2[2(-1-8) + (12-2)] = [-9 + 12 + 4] + 2[-18 + 10] = 7+2(-8)= -9