Download presentation

Presentation is loading. Please wait.

Published byBarrett Osgood Modified over 3 years ago

2
Determinant The numerical value of a square array of numbers that can be used to solve systems of equations with matrices. Second-Order Determinant (of a 2 x 2 Matrix) The word with the matrix symbol The Determinant symbol (Criss-Cross & multiply then subtract)

3
Example 1

4
nth-Order Determinant The determinant of any n x n (square) matrix Third-Order Determinant (of a 3 x 3 Matrix) Determinant of what’s left Signs alternate, beginning with minus Then simplify

5
Example 2 Select any row & column, then calculate the determinant with expansion of the minors

6
Identity Matrix for Multiplication A square matrix, that when multiplied with another square matrix, results in a matrix with no change. The square matrix always consists of 1’s on the diagonal beginning with the first element; the remaining elements are zeros.

7
Inverse Matrix (A -1 ) A matrix that when multiplied by another matrix results in the identity matrix. Note: Not all matrices have an inverse – If the determinant of the original matrix has a value of zero, A -1 does not exist

8
Example 3 Determine if a matrix exists (Det ≠ 0) 4 2 3 -4 Switch places Same place Switch Signs The inverse is used to solve systems of equations with matrices.

9
Calculate the determinant: Determine the inverse: Multiply each side of the matrix equation by the inverse & solve:

10
Example 5 Define the variables: Let x = amount of 10% bond Let y = amount of 6% bond Two variables, two equations: x + y = 10,500 Simplify; no decimals. Write matrix equation:Determine the inverse: 1(-5) – 3(1) = -8 3x – 5y = 0

11
HW: Page 102

Similar presentations

OK

Linear System of Simultaneous Equations Warm UP First precinct: 6 arrests last week equally divided between felonies and misdemeanors. Second precinct:

Linear System of Simultaneous Equations Warm UP First precinct: 6 arrests last week equally divided between felonies and misdemeanors. Second precinct:

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on trans-siberian railway prices Ppt on accidents in india Ppt on product life cycle with examples Ppt on review of related literature about study Ppt on latest technology 2012 Science ppt on electricity for class 10th Topics for ppt on environmental management Business plan template free download ppt on pollution Ppt on covering the environmental problems causes effects and solutions Download ppt on pulse code modulation ppt