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### The Span of a Set of Vectors

00:17:06Patrick JonesThe Span of a Set of Vectors. In this video, I look at the notion of a span of a vector set. I work in R2 just to keep things simple, but the results can be generalized! I show how to justify that two vectors do in fact span all of R2.

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### Determinants to Find the Area of a Polygon

00:03:35Patrick JonesDeterminants to Find the Area of a Polygon - In this video, I show how one can use determinants to find the area enclosed by any polygon!

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### Determinants to Find the Area of a Triangle

00:02:44Patrick JonesDeterminants to Find the Area of a Triangle - In this video, I show how one can use determinants to find the area of a triangle.

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### Determinant of a 2 x 2 Matrix - A Few Basic Questions

00:02:45Patrick JonesDeterminant of a 2 x 2 Matrix - A Few Basic Questions. In this video, I show how to find the determinant of a 2 x 2 matrix, and do a few related problems.

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### Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors - Example 1

00:06:46Patrick JonesFinding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors - Example 1. Besides using row reduction, this is another way to find the inverse of a 3 x 3 matrix.

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### Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors - Example 2

00:07:14Patrick JonesFinding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors - Example 2. Besides using row reduction, this is another way to find the inverse of a 3 x 3 matrix.

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### Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors - Example 3

00:05:28Patrick JonesFinding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors - Example 3. Besides using row reduction, this is another way to find the inverse of a 3 x 3 matrix.

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### Cramer's Rule to Solve a System of 3 Linear Equations - Example 1

00:10:50Patrick JonesCramer's Rule to Solve a System of 3 Linear Equations - Example 1

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### Cramer's Rule to Solve a System of 3 Linear Equations - Example 2

00:09:39Patrick JonesCramer's Rule to Solve a System of 3 Linear Equations - Example 2

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### Using Gauss-Jordan to Solve a System of Three Linear Equations - Example 1

00:07:12Patrick JonesUsing Gauss-Jordan to Solve a System of Three Linear Equations - Example 1

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### Using Gauss-Jordan to Solve a System of Three Linear Equations - Example 2

00:05:37Patrick JonesUsing Gauss-Jordan to Solve a System of Three Linear Equations - Example 2

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### Solving a 3 x 3 System of Equations Using the Inverse

00:09:01Patrick JonesSolving a 3 x 3 System of Equations Using the Inverse. In this video, I solve a system of three linear equations by using the inverse.

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### Solving a Dependent System of Linear Equations involving 3 Variables

00:09:46Patrick JonesSolving a Dependent System of Linear Equations involving 3 Variables

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### Systems of Linear Equations - Inconsistent Systems Using Elimination by Addition - Example 1

00:03:43Patrick JonesSystems of Linear Equations - Inconsistent Systems Using Elimination by Addition - Example 1

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### Systems of Linear Equations - Inconsistent Systems Using Elimination by Addition - Example 2

00:04:02Patrick JonesSystems of Linear Equations - Inconsistent Systems Using Elimination by Addition - Example 2

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### Systems of Linear Equations - Inconsistent Systems Using Elimination by Addition - Example 3

00:03:03Patrick JonesSystems of Linear Equations - Inconsistent Systems Using Elimination by Addition - Example 3

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### Solving a System of Equations Involving 3 Variables Using Elimination by Addition - Example 1

00:06:46Patrick JonesSolving a System of Equations Involving 3 Variables Using Elimination by Addition - Example 1. There are TONS of fractions, so I hope you do not get drowned out with all the arithmetic!!

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### Solving a System of Equations Involving 3 Variables Using Elimination by Addition - Example 2

00:04:15Patrick JonesSolving a System of Equations Involving 3 Variables Using Elimination by Addition - Example 2. There are TONS of fractions, so I hope you do not get drowned out with all the arithmetic!!

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### Solving a System of Equations Involving 3 Variables Using Elimination by Addition - Example 3

00:08:17Patrick JonesSolving a System of Equations Involving 3 Variables Using Elimination by Addition - Example 2. There are TONS of fractions, so I hope you do not get drowned out with all the arithmetic!!

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### Finding the Determinant of a 3 x 3 matrix

00:06:56Patrick JonesFinding the Determinant of a 3 x 3 matrix. I show the basic formula and compute the determinant of a specific matrix.

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### Row Reducing a Matrix - Systems of Linear Equations - Part 1

00:09:59Patrick JonesRow Reducing a Matrix - Systems of Linear Equations - Part 1. Basic notation and procedure as well as a full example are shown. The last part of the second part got cut off, but is finished in another video!!!

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### Row Reducing a Matrix - Systems of Linear Equations - Part 2

00:05:34Patrick JonesRow Reducing a Matrix - Systems of Linear Equations - Part 2 - This is a follow up to Part 1 where the last example was cut off!

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### Solving Systems of Equations Using Elimination By Addition

00:09:59Patrick JonesSolving Systems of Linear Equations Using Elimination By Addition - Two complete examples and part of a third problem are shown!

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### Multiplying Matrices - Example 1

00:09:38Patrick JonesMultiplying Matrices - Two examples of multiplying a matrix by another matrix are shown.

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### Matrix Operations

00:05:25Patrick JonesMatrix Operations - Adding, Subtracting, and Multiplying by a constant for matrices is discussed.

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### An Introduction to the Dot Product

00:04:06Patrick JonesAn Introduction to the Dot Product. In this video, I give the formula for the dot product of two vectors, discuss the geometric meaning of the dot product, and find the dot product between some vectors.

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### Sketching Sums and Differences of Vectors

00:03:22Patrick JonesSketching Sums and Differences of Vectors. In this video, I give three vectors, and do a few examples of sketching the sum and difference of those vectors.

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### Word Problems Involving Velocity or Other Forces (Vectors), Ex 1

00:03:10Patrick JonesWord Problems Involving Velocity or Other Forces (Vectors), Ex 1. In this problem we do a word problem involving the bearing (direction) of a boat.

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### Word Problems Involving Velocity or Other Forces (Vectors), Ex 2

00:11:29Patrick JonesWord Problems Involving Velocity or Other Forces (Vectors), Ex 2. In this problem we are given the bearing and velocity of a plane and the bearing and velocity of the wind; we want to find out the actual velocity of the plane after taking the wind into consideration. (a nice little problem!)

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### Word Problems Involving Velocity or Other Forces (Vectors), Ex 3.

00:02:10Patrick JonesWord Problems Involving Velocity or Other Forces (Vectors), Ex 3. Here we know the force required to keep a box from sliding down a ramp; we want to know the angle of inclination of the ramp.

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### Finding a Unit Vector, Ex 1

00:02:07Patrick JonesFinding a Unit Vector, Ex 1. In this video I discuss the idea of a unit vector and show how to find it (divide the vector by its magnitude!).

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### Finding a Unit Vector, Ex 2

00:04:55Patrick JonesFinding a Unit Vector, Ex 2. In this video we find a unit vector associated with a given vector.

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### Finding the Components of a Vector, Ex 1

00:02:38Patrick JonesFinding the Components of a Vector, Ex 1. In this video, we are given the magnitude and direction angle for the vector and want to express the vector in component form.

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### Finding the Components of a Vector, Ex 2

00:06:34Patrick JonesFinding the Components of a Vector, Ex 2. In this video, we are given the magnitude and direction angle for the vector and want to express the vector in component form.

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### Vector Addition and Scalar Multiplication, Example 1

00:03:24Patrick JonesVector Addition and Scalar Multiplication, Example 1. In this video, we look at vector addition and scalar multiplication algebraically using the component form of the vector. I do not graph the vectors in this video (but do in others).

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### Vector Addition and Scalar Multiplication, Example 2

00:03:51Patrick JonesVector Addition and Scalar Multiplication, Example 2. In this video I add two vectors in component form and also sketch the vectors to illustrate how to add vectors graphically (very useful stuff!).

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### Magnitude and Direction of a Vector, Example 1

00:03:57Patrick JonesMagnitude and Direction of a Vector, Example 1. Here we find the magnitude (length) of some vectors and find the angle associated with them.

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### Magnitude and Direction of a Vector, Example 2

00:03:46Patrick JonesMagnitude and Direction of a Vector, Example 2. Here we find the magnitude (length) of some vectors and find the angle associated with them.

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### Magnitude and Direction of a Vector, Example 3

00:06:04Patrick JonesMagnitude and Direction of a Vector, Example 3. Here we find the magnitude (length) of one last vector and find the angle associated with them.

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### When Are Two Vectors Considered to Be the Same?

00:02:03Patrick JonesWhen are two vectors considered to be the same?

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### An Introduction to Vectors, Part 1

00:04:46Patrick JonesAn introduction to vectors: magnitude, direction, length, component form are all discussed.

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### Finding the Vector Equation of a Line

00:07:41Patrick JonesFinding the Vector Equation of a Line - In this video, I give the formula to find the vector equation of a line and do two examples.

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### Vector Basics - Algebraic Representations

00:06:16Patrick JonesVector Basics - Components, adding vectors algebraically and multiplying by a constant.

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### Vector Basics - Algebraic Representations Part 2

00:05:35Patrick JonesVector Basics - Components, adding vectors algebraically and multiplying by a constant. PART 2 of the video that got cut off!!

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### Vector Basics - Drawing Vectors/ Vector Addition

00:11:32Patrick JonesVector Basics - Drawing Vectors/ Vector Addition. In this video, I discuss the basic notion of a vector, and how to add vectors together graphically as well as what it means graphically to multiply a vector by a scalar.

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### Vectors - The Dot Product

00:07:26Patrick JonesVectors - The Dot Product. I show how to compute the dot product of two vectors, along with some useful theorems and results involving dot products. 3 complete examples are shown.

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### Vectors - Finding Magnitude or Length

00:03:32Patrick JonesVectors - Finding Magnitude or Length. I give the formula, and do a couple examples of finding the magitude, or length, or a vector. Nothing heavy!

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### Linear Independence and Linear Dependence, Ex 1

00:08:05Patrick JonesLinear Independence and Linear Dependence, Ex 1. In this video, I explore the idea of what it means for a set of vectors to be linearly independent or dependent. I then work an example showing that a set of vectors is linearly dependent.

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### Linear Independence and Linear Dependence, Ex 2

00:06:46Patrick JonesLinear Independence and Linear Dependence, Ex 2. As a follow up to Ex 1, I show a set of vectors that is linearly independent by using row reduction.

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### Homogeneous Systems of Linear Equations - Trivial and Nontrivial Solutions, Part 1

00:09:09Patrick JonesHomogeneous Systems of Linear Equations - Trivial and Nontrivial Solutions, Part 1. In this video, I show what a homogeneous system of linear equations is, and show what it means to have only trivial solutions. In the next video, I work out an example that has nontrivial solutions.

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### Homogeneous Systems of Linear Equations - Trivial and Nontrivial Solutions, Part 2

00:10:32Patrick JonesHomogeneous Systems of Linear Equations - Trivial and Nontrivial Solutions, Part 2. In this video, I show how to find solutions to a homogeneous system of linear equations that has nontrivial solutions.

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### Useful Things to Remember About Linearly Independent Vectors

00:04:41Patrick JonesUseful Things to Remember About Linearly Independent Vectors. Just a few things that I think are useful to remember about linearly independent and dependent sets of vectors!

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### Basis for a Set of Vectors

00:11:43Patrick JonesBasis for a Set of Vectors. In this video, I give the definition for a apos; basis apos; of a set of vectors. I think proceed to work an example that shows three vectors that I picked form a basis for R_3.

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### Procedure to Find a Basis for a Set of Vectors

00:07:17Patrick JonesProcedure to Find a Basis for a Set of Vectors. In this video, I start with a set of vectors in R_3 and find a basis for those vectors. The basis is NOT necessarily unique!

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### Linear Transformations , Example 1, Part 1 of 2

00:09:06Patrick JonesLinear Transformations , Example 1, Part 1 of 2. In this video, I introduce the idea of a linear transformation of vectors from one space to another. I then proceed to show an example of whether or not a particular transformation is linear or not.

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### Linear Transformations , Example 1, Part 2 of 2

00:04:56Patrick JonesLinear Transformations , Example 1, Part 2 of 2. In this video, I introduce the idea of a linear transformation of vectors from one space to another. I then proceed to finish an example of whether or not a particular transformation is linear or not.

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