1 / 14

Chapter 8 Matrices and Determinants

Chapter 8 Matrices and Determinants. By Richard Warner, Nate Huyser , Anastasia Sanderson, Bailey Grote. Chapter 8.1: General Matrices. Rectangular array of numbers called entries Dimensions of a matrix are number of rows by the number of columns. Chapter 8.1: Augmented Matrices.

cael
Download Presentation

Chapter 8 Matrices and Determinants

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. Chapter 8Matrices and Determinants By Richard Warner, Nate Huyser, Anastasia Sanderson, Bailey Grote

  2. Chapter 8.1: General Matrices • Rectangular array of numbers called entries • Dimensions of a matrix are number of rows by the number of columns

  3. Chapter 8.1: Augmented Matrices • Augmented Matrix- derived from a system of equations • Elementary Row Operations • Interchange any two rows • Multiply any row by a nonzero constant • Add two rows together • 2x2 by hand, 3x3 with calculator

  4. Chapter 8.1: Reduced Row Echelon Form (RREF) • Any rows consisting of all zeros occur at the bottom of the matrix • All entries on the main diagonal are 1 • All entries not on the main diagonal or in the last column are 0 • A13 is the x-coordinate of the solution • A23 is the y-coordinate of the solution

  5. Chapter 8.1: Gauss Jordan Elimination • Uses Augmented Matrices to solve systems of equations • Write system as an augmented matrix • Use the row operations to make A11 = 1 • Work down, around, and up to achieve RREF • Write last column as ordered pair for final answer

  6. Chapter 8.1: Solving with Calculator (RREF) • Only used for Matrices larger than 2x2 • (2nd) [Matrix] → EDIT • Matrix[A] 3x4 • Enter entries by rows • (2nd) [Quit] • (2nd) [Matrix] → MATH • Select [RREF] • (2nd) [Matrix] select Martix[A]

  7. Chapter 8.2: Matrix Operations Equality of Matrices: 2 matrices are equal if they have the same dimensions and their corresponding entries are equal To add and subtract Matrices: They must have the same dimensions. Add the corresponding entries Scalar Multiplication: Multiplying a matrix by a scalar (constant) Multiply each entry in the matrix by the scalar

  8. Chapter 8.2: Matrix Operations Matrix Multiplication: • To Multiply AB, A’s columns must equal B’s rows • Multiply the entries in A’s rows by the corresponding entries in B’s columns • Amxn* Bnxr=ABmxr Ex: p.598 #29

  9. Identity Matrices 8.3 Inverse Matrices I 2x2 I 3x3

  10. Cont. 8.3 Inverse Multiplication • A A-1 =A-1 A =I • If A= where ad-bc cannot equal 0, Then A-1 =1/(ad-bc) * Inverse of2x2:

  11. Cont. 8.3 Inverse Multiplication Inverse of 3x3 • Enter [matrix] in calculator • [matrix][A] [enter] [x-1 ] [enter] To solve a system of linear equations • Write the system of equations as a matrix problem • Find A-1 • X=A1B x =

  12. 8.4 Determinants • a real number derived from a square matrix • If A = then Det[A]= AD-CB • For 2x2 matrices only • For 3x3 matrices or larger • (2nd) Matrix → [Edit] A • Enter dimensions • (2nd) Quit • (2nd) Matrix → [Math] enter • (2nd) Matrix → enter

  13. 8.5 Determinant Applications • Cramer’s Rule solves systems using determinates. • Example:

  14. 8.5 Determinant Applications • Finding the area of a triangle where the points are (a,b), (c,d), (e,f) • Points are collinear if A=0

More Related