1 / 13

Sullivan Algebra and Trigonometry: Section 12.4

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.

mnicholas
Download Presentation

Sullivan Algebra and Trigonometry: Section 12.4

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 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

  2. Theorem Cramer’s Rule

  3. 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

  4. When evaluating a determinant, you can expand across any row or down any column you choose.

  5. Cramer’s Rule for Three Equations Containing Three Variables provided

  6. Solution: x = 2, y = -1, z = 3

  7. 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.

More Related