130 likes | 143 Views
Sullivan Algebra and Trigonometry: Section 12.4. Objectives of this Section Evaluate 2 by 2 and 3 by 3 Determinants Use Cramer’s Rule to Solve a System of Two or Three Equations With Two or Three Variables Know Properties of Determinants. Theorem Cramer’s Rule.
E N D
Sullivan Algebra and Trigonometry: Section 12.4 • Objectives of this Section • Evaluate 2 by 2 and 3 by 3 Determinants • Use Cramer’s Rule to Solve a System of Two or Three Equations With Two or Three Variables • Know Properties of Determinants
If D = 0, then the system has infinitely many solutions or is inconsistent and therefore has no solution. A 3 by 3 determinant is symbolized by
When evaluating a determinant, you can expand across any row or down any column you choose.
Cramer’s Rule for Three Equations Containing Three Variables provided
Properties of Determinants 1. The value of the determinant changes sign if any two rows or columns are interchanged. 2. If any row or any column of a determinant is multiplied by a non-zero number k, the value of the determinant is also changed by a factor of k. 3. If the entries of any row or any column of a determinant are multiplied by a non-zero number k and the result is added to the corresponding entries of another row or another column, the value of the determinant remains unchanged.