Solution. Find the determinantof

Example 5

Find the determinantof

[A]=

Remember earlier in this chapter, we conducted the steps of forward elimination of unknowns using Naïve GaussEliminationmethod on [A] to give

According to Theorem 2

det (A) = det (B)

What if I cannot find the determinantof the matrixusing Naive GaussEliminationmethod, for example, if I get division by zero problems during Naïve Gauss Elimination method?

Well, you can apply GaussianElimination with Partial Pivoting. However, the determinantof the resulting upper triangular matrixmay differ by a sign. The following theorem applies in addition to the previous two to find determinant of a square matrix.

Theorem 3:

Let [ A ] be a n x n matrix. Then, if [ B ] is a matrix that results from switching one row with another row, then det (B) = - det (A).

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