Episode Synopsis "A.4: Inconsistent Linear Systems and Systems with Infinitely Many Solutions - 07) Alternative Theorem and Proof"

A.4: Inconsistent Linear Systems and Systems with Infinitely Many Solutions

Listen "A.4: Inconsistent Linear Systems and Systems with Infinitely Many Solutions - 07) Alternative Theorem and Proof"

More episodes of the podcast Combined Calculus (Appendix, Chapters 0 - 1)

• A.4: Inconsistent Linear Systems and Systems with Infinitely Many Solutions - 16) Verifying RREF and Writing Solution (Cont’d)
• A.4: Inconsistent Linear Systems and Systems with Infinitely Many Solutions - 17) Verifying RREF and Writing Solution (Cont’d)
• A.4: Inconsistent Linear Systems and Systems with Infinitely Many Solutions - 18) Another Example with 4x5 Matrix
• A.4: Inconsistent Linear Systems and Systems with Infinitely Many Solutions - 19) Another 4x5 Matrix
• A.4: Inconsistent Linear Systems and Systems with Infinitely Many Solutions - 20) Final 4x5 Matrix
• A.4: Inconsistent Linear Systems and Systems with Infinitely Many Solutions - 21) Summary of Chapter 2
• A.4: Inconsistent Linear Systems and Systems with Infinitely Many Solutions - 11) Example from Book-4 Variables
• A.4: Inconsistent Linear Systems and Systems with Infinitely Many Solutions - 12) Example from Book-4 Variables
• A.4: Inconsistent Linear Systems and Systems with Infinitely Many Solutions - 13) Calculator Tip-RREF
• A.4: Inconsistent Linear Systems and Systems with Infinitely Many Solutions - 14) “Word Problem” using Calculator
• A.4: Inconsistent Linear Systems and Systems with Infinitely Many Solutions - 15) Verifying RREF and Writing Solution
• A.4: Inconsistent Linear Systems and Systems with Infinitely Many Solutions - 06) Types of Solutions in 3 Variables (Cont’d)
• A.4: Inconsistent Linear Systems and Systems with Infinitely Many Solutions - 07) Alternative Theorem and Proof
• A.4: Inconsistent Linear Systems and Systems with Infinitely Many Solutions - 08) Inconsistent Systems-3 Variables
• A.4: Inconsistent Linear Systems and Systems with Infinitely Many Solutions - 09) Infinitely Many Solutions-2 Variables
• A.4: Inconsistent Linear Systems and Systems with Infinitely Many Solutions - 10) Infinitely Many Solutions-3 Variables
• A.3: Gauss-Jordan Row Reduction - 15) Row Operations on the TI-89
• A.3: Gauss-Jordan Row Reduction - 16) G-JRR on Calculator
• A.3: Gauss-Jordan Row Reduction - 17) Using GJ-RR to find A-1 on TI-89
• A.3: Gauss-Jordan Row Reduction - 18) Discussion About Memory
• A.4: Inconsistent Linear Systems and Systems with Infinitely Many Solutions - 01) Introduction to Inconsistent System
• A.4: Inconsistent Linear Systems and Systems with Infinitely Many Solutions - 02) RREF Form and Inconsistent Systems
• A.4: Inconsistent Linear Systems and Systems with Infinitely Many Solutions - 03) 2x2 System w/ Infinitely Many Solutions
• A.4: Inconsistent Linear Systems and Systems with Infinitely Many Solutions - 04) Types of Solutions to Systems of Linear Equations in 2 Variables
• A.4: Inconsistent Linear Systems and Systems with Infinitely Many Solutions - 05) Possible Types of Solutions in 3 Variables
• A.3: Gauss-Jordan Row Reduction - 09) 3-Variable Example of G-JRR
• A.3: Gauss-Jordan Row Reduction - 10) Using G-JRR to find A-1
• A.3: Gauss-Jordan Row Reduction - 11) Finding 3x3 Inverse
• A.3: Gauss-Jordan Row Reduction - 12) Finding Another 3x3 Inverse
• A.3: Gauss-Jordan Row Reduction - 13) Summary of 2.3
• A.3: Gauss-Jordan Row Reduction - 14) What’s to Come in 2.4
• A.3: Gauss-Jordan Row Reduction - 01) Introductory Problem
• A.3: Gauss-Jordan Row Reduction - 02) Intro.to Augmented Matrix
• A.3: Gauss-Jordan Row Reduction - 03) A General Augmented Matrix
• A.3: Gauss-Jordan Row Reduction - 04) Elimination Needed for Gauss-Jordan Row Reduction
• A.3: Gauss-Jordan Row Reduction - 05) Checking Solution from Video 4
• A.3: Gauss-Jordan Row Reduction - 06) Gauss-Jordan Row Reduction [G-JRR] on Example from Video 4
• A.3: Gauss-Jordan Row Reduction - 07) 2-Variable Example of G-JRR
• A.3: Gauss-Jordan Row Reduction - 08) 3-Variable Example of G-JRR
• A.2: Matrix Multiplication - 14) Properties of Matrices
• A.2: Matrix Multiplication - 15) Matrices, Systems of Equations, and AX=B
• A.2: Matrix Multiplication - 16) Solving 2x2 System using AX=B
• A.2: Matrix Multiplication - 17) Summary of Previous Solution
• A.2: Matrix Multiplication - 18) Solve 3x3 System Using AX=B
• A.2: Matrix Multiplication - 19) Definition AT (Transpose)
• A.2: Matrix Multiplication - 20) Practice AT
• A.2: Matrix Multiplication - 21) Calculator: Vector Multiplication
• A.2: Matrix Multiplication - 22) Calculator: Matrix Multiplication
• A.2: Matrix Multiplication - 11) Matrix Mult: Discovering I
• A.2: Matrix Multiplication - 12) Matrix Mult: Inverses
• A.2: Matrix Multiplication - 13) Matrix Mult: Showing Inverse
• A.2: Matrix Multiplication - 03) Vector Mult: (Cont’d)
• A.2: Matrix Multiplication - 04) Vector Mult: Practice
• A.2: Matrix Multiplication - 05) Matrix Mult: (1x3)(3x2)
• A.2: Matrix Multiplication - 06) Matrix Mult: (3x3)(3x2) and General Notation
• A.2: Matrix Multiplication - 07) Matrix Mult: (2x3)(3x2)
• A.2: Matrix Multiplication - 08) Matrix Mult: AB vs. BA
• A.2: Matrix Multiplication - 09) Matrix Mult: Practice w/ Dimensions
• A.2: Matrix Multiplication - 10) Matrix Mult: (2,3) entry
• A.1: Basic Operations - 03) Matrices: 3-Variable Example
• A.1: Basic Operations - 04) Basic Operations and Definitions
• A.1: Basic Operations - 05) Dimension
• A.1: Basic Operations - 06) Matrix Addition and Scalar Multiplication
• A.1: Basic Operations - 07) Practice on Scalar Multiplication, Zero Matrix
• A.1: Basic Operations - 08) Problems Similar to Homework
• A.1: Basic Operations - 09) Problems Similar to Homework 2
• A.1: Basic Operations - 10) Problem from Homework
• A.2: Matrix Multiplication - 01) Introduction
• A.2: Matrix Multiplication - 02) Vector Multiplication-2 Examples
• A.1: Basic Operations - 01) Matrices: Application from Business
• A.1: Basic Operations - 02) Matrices: Application from Business 2
• Chapter 1.8: Regression - 02) Example 1
• Chapter 1.8: Regression - 03) Example 2
• Chapter 1.8: Regression - 04) Calculator Tips
• Chapter 1.7: More on Functions - 05) Example 5
• Chapter 1.7: More on Functions - 06) Example 6
• Chapter 1.7: More on Functions - 07) Example 7
• Chapter 1.7: More on Functions - 08) Example 8
• Chapter 1.7: More on Functions - 09) Example 9
• Chapter 1.7: More on Functions - 10) Exampe 10
• Chapter 1.7: More on Functions - 11) Symmetry
• Chapter 1.7: More on Functions - 12) Using Zeros
• Chapter 1.7: More on Functions - 13) Translations
• Chapter 1.8: Regression - 01) Data Points
• Chapter 1.7: More on Functions - 04) Example 4
• Chapter 1.7: More on Functions - 03) Example 3
• Chapter 1.6: Economic Functions - 04) Example 4
• Chapter 1.6: Economic Functions - 05) Example 5
• Chapter 1.6: Economic Functions - 06) Example 7
• Chapter 1.6: Economic Functions - 07) Marginal Function
• Chapter 1.6: Economic Functions - 08) Demand Function
• Chapter 1.6: Economic Functions - 09) Revenue
• Chapter 1.6: Economic Functions - 10) Calculator Tips
• Chapter 1.7: More on Functions - 01) Example 1
• Chapter 1.7: More on Functions - 02) Example 2
• Chapter 1.5: The Circle - 05) Example 6
• Chapter 1.5: The Circle - 06) Tangent Line 1
• Chapter 1.5: The Circle - 07) Tangent Line 2
• Chapter 1.5: The Circle - 08) Tangent Line 3
• Chapter 1.5: The Circle - 09) Ellipse, Figure 6
• Chapter 1.5: The Circle - 10) Ellipse, standard form
• Chapter 1.5: The Circle - 11) Calculator Tips
• Chapter 1.6: Economic Functions - 01) Example 1
• Chapter 1.6: Economic Functions - 02) Example 2
• Chapter 1.6: Economic Functions - 03) Example 3
• Chapter 1.5: The Circle - 04) Examples 3,4 and 5
• Chapter 1.4: Quadratic Functions - 08) Example 5
• Chapter 1.4: Quadratic Functions - 09) Example 6
• Chapter 1.4: Quadratic Functions - 10) Example 7
• Chapter 1.4: Quadratic Functions - 11) Calculator Tips
• Chapter 1.5: The Circle - 01) The Circle
• Chapter 1.5: The Circle - 02) Example 1
• Chapter 1.5: The Circle - 03) Example 2
• Chapter 1.3: Applications of Linear Functions - 04) Linear Functions
• Chapter 1.3: Applications of Linear Functions - 05) Depreciation
• Chapter 1.4: Quadratic Functions - 01) Quadratic Functions
• Chapter 1.4: Quadratic Functions - 02) Figure 5
• Chapter 1.4: Quadratic Functions - 03) Horizontal Translation
• Chapter 1.4: Quadratic Functions - 04) Example 1
• Chapter 1.4: Quadratic Functions - 05) Completing square - standard form
• Chapter 1.4: Quadratic Functions - 06) General procedure - standard form
• Chapter 1.4: Quadratic Functions - 07) Example 3
• Chapter 1.3: Applications of Linear Functions - 01) Example 1
• Chapter 1.3: Applications of Linear Functions - 02) Example 2
• Chapter 1.3: Applications of Linear Functions - 03) Example 3
• Chapter 1.2: Basic Notions of Functions - 08) Example 13
• Chapter 1.2: Basic Notions of Functions - 09) Example 14
• Chapter 1.2: Basic Notions of Functions - 10) Example 16
• Chapter 1.2: Basic Notions of Functions - 11) Rationalize Denominator
• Chapter 1.2: Basic Notions of Functions - 12) Calculator Tips
• Chapter 1.2: Basic Notions of Functions - 13) Calculator Tips 2
• Chapter 1.1: The Line - 04) Example 3
• Chapter 1.1: The Line - 05) Example 4
• Chapter 1.1: The Line - 06) Example 6
• Chapter 1.1: The Line - 07) Perpendicular Lines
• Chapter 1.2: Basic Notions of Functions - 01) Example 1
• Chapter 1.2: Basic Notions of Functions - 02) Example 4
• Chapter 1.2: Basic Notions of Functions - 03) Example 5
• Chapter 1.2: Basic Notions of Functions - 04) Example 7
• Chapter 1.2: Basic Notions of Functions - 05) Example 10
• Chapter 1.2: Basic Notions of Functions - 06) Example 11
• Chapter 1.2: Basic Notions of Functions - 07) Example 12
• Chapter 1.1: The Line - 01) Example 1
• Chapter 1.1: The Line - 02) Example 1, pt.2
• Chapter 1.1: The Line - 03) Example 2
• Chapter 0.5: Solving Non-Linear Inequalities - 08) Solving Inequalities 2
• Chapter 0.4: The Quadratic Formula and Applications - 07) Example 8
• Chapter 0.4: The Quadratic Formula and Applications - 08) Example 9
• Chapter 0.4: The Quadratic Formula and Applications - 09) Quadratic Formula
• Chapter 0.5: Solving Non-Linear Inequalities - 01) Example 1
• Chapter 0.5: Solving Non-Linear Inequalities - 02) Example 2
• Chapter 0.5: Solving Non-Linear Inequalities - 03) Example 3
• Chapter 0.5: Solving Non-Linear Inequalities - 04) Example 4
• Chapter 0.5: Solving Non-Linear Inequalities - 05) Example 5
• Chapter 0.5: Solving Non-Linear Inequalities - 06) Example 6
• Chapter 0.5: Solving Non-Linear Inequalities - 07) Solving Inequalities
• Chapter 0.3: Completing the Square - 04) Example 7
• Chapter 0.3: Completing the Square - 05) Completing the Square
• Chapter 0.4: The Quadratic Formula and Applications - 01) Example 1
• Chapter 0.4: The Quadratic Formula and Applications - 02) Example 2
• Chapter 0.4: The Quadratic Formula and Applications - 03) Example 3
• Chapter 0.4: The Quadratic Formula and Applications - 04) Example 4
• Chapter 0.4: The Quadratic Formula and Applications - 05) Example 5
• Chapter 0.4: The Quadratic Formula and Applications - 06) Example 7
• Chapter 0.1: Solving Linear Equations - 11) Example 15
• Chapter 0.1: Solving Linear Equations - 12) Calculator
• Chapter 0.2: Solving Equations of the form ax^2 - b =0 - 01) Lesson
• Chapter 0.2: Solving Equations of the form ax^2 - b =0 - 02) Example 1
• Chapter 0.2: Solving Equations of the form ax^2 - b =0 - 03) Example 2
• Chapter 0.2: Solving Equations of the form ax^2 - b =0 - 04) Example 5
• Chapter 0.2: Solving Equations of the form ax^2 - b =0 - 05) Example 6
• Chapter 0.3: Completing the Square - 01) Example 2
• Chapter 0.3: Completing the Square - 02) Example 5
• Chapter 0.3: Completing the Square - 03) Example 6
• Chapter 0.1: Solving Linear Equations - 01) Examples 1 and 2
• Chapter 0.1: Solving Linear Equations - 02) Example 3
• Chapter 0.1: Solving Linear Equations - 03) Example 5
• Chapter 0.1: Solving Linear Equations - 04) Example 6
• Chapter 0.1: Solving Linear Equations - 05) Example 9
• Chapter 0.1: Solving Linear Equations - 06) Example 10
• Chapter 0.1: Solving Linear Equations - 07) Example 11
• Chapter 0.1: Solving Linear Equations - 08) Example 12
• Chapter 0.1: Solving Linear Equations - 09) Example 13
• Chapter 0.1: Solving Linear Equations - 10) Example 14