Complete Quick Lessons on Linear Algebra

Video Lectures

Displaying all 58 video lectures.
Lecture 1
The Span of a Set of Vectors
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The Span of a Set of Vectors
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The 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.
Lecture 2
Determinants to Find the Area of a Polygon
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Determinants to Find the Area of a Polygon
Determinants 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!
Lecture 3
Determinants to Find the Area of a Triangle
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Determinants to Find the Area of a Triangle
Determinants to Find the Area of a Triangle - In this video, I show how one can use determinants to find the area of a triangle.
For more free math videos, visit http://PatrickJMT.com
Lecture 4
Solving a 3 x 3 System of Equations Using the Inverse
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Solving a 3 x 3 System of Equations Using the Inverse
Solving 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.
For more free math videos, visit http://PatrickJMT.com
Lecture 5
Determinant of a 2 x 2 Matrix - A Few Basic Questions
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Determinant of a 2 x 2 Matrix - A Few Basic Questions
Determinant 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.
For more free math videos, visit http://PatrickJMT.com
Lecture 6
Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors - Example 3
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Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors - Example 3
Finding 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.
Lecture 7
Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors - Example 2
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Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors - Example 2
Finding 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.
Lecture 8
Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors - Example 1
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Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors - Example 1
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Finding 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.
Lecture 9
Cramer's Rule to Solve a System of 3 Linear Equations - Example 2
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Cramer's Rule to Solve a System of 3 Linear Equations - Example 2
Cramer's Rule to Solve a System of 3 Linear Equations - Example 2
Lecture 10
Cramer'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 1
Cramer's Rule to Solve a System of 3 Linear Equations - Example 1
Lecture 11
Using Gauss-Jordan to Solve a System of Three Linear Equations - Example 2
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Using Gauss-Jordan to Solve a System of Three Linear Equations - Example 2
Using Gauss-Jordan to Solve a System of Three Linear Equations - Example 2
Lecture 12
Using 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 1
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Using Gauss-Jordan to Solve a System of Three Linear Equations - Example 1
Lecture 13
Solving a Dependent System of Linear Equations involving 3 Variables
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Solving a Dependent System of Linear Equations involving 3 Variables
Solving a Dependent System of Linear Equations involving 3 Variables
Lecture 14
Systems of Linear Equations - Inconsistent Systems Using Elimination by Addition - Example 3
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Systems of Linear Equations - Inconsistent Systems Using Elimination by Addition - Example 3
Systems of Linear Equations - Inconsistent Systems Using Elimination by Addition - Example 3
Lecture 15
Systems 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 2
Systems of Linear Equations - Inconsistent Systems Using Elimination by Addition - Example 2
Lecture 16
Systems 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 1
Systems of Linear Equations - Inconsistent Systems Using Elimination by Addition - Example 1
Lecture 17
Solving a System of Equations Involving 3 Variables Using Elimination by Addition - Example 3
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Solving a System of Equations Involving 3 Variables Using Elimination by Addition - Example 3
Solving 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!!
Lecture 18
Solving a System of Equations Involving 3 Variables Using Elimination by Addition - Example 2
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Solving a System of Equations Involving 3 Variables Using Elimination by Addition - Example 2
Solving 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!!
Lecture 19
Solving a System of Equations Involving 3 Variables Using Elimination by Addition - Example 1
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Solving a System of Equations Involving 3 Variables Using Elimination by Addition - Example 1
Solving 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!!
Lecture 20
Finding the Determinant of a 3 x 3 matrix
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Finding the Determinant of a 3 x 3 matrix
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Finding the Determinant of a 3 x 3 matrix. I show the basic formula and compute the determinant of a specific matrix.
For more free math videos, visit http://PatrickJMT.com
Lecture 21
Row Reducing a Matrix - Systems of Linear Equations - Part 2
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Row Reducing a Matrix - Systems of Linear Equations - Part 2
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Row Reducing a Matrix - Systems of Linear Equations - Part 2 - This is a follow up to Part 1 where the last example was cut off! For more free math videos, visit http://PatrickJMT.com

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Lecture 22
Row Reducing a Matrix - Systems of Linear Equations - Part 1
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Row Reducing a Matrix - Systems of Linear Equations - Part 1
Row 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!!! For more free math videos, visit http://PatrickJMT.com

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Lecture 23
Solving Systems of Equations Using Elimination By Addition
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Solving Systems of Equations Using Elimination By Addition
Solving Systems of Linear Equations Using Elimination By Addition - Two complete examples and part of a third problem are shown! For more free math videos, visit http://PatrickJMT.com
Lecture 24
Multiplying Matrices - Example 1
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Multiplying Matrices - Example 1
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Multiplying Matrices - Two examples of multiplying a matrix by another matrix are shown. For more free math videos, visit http://PatrickJMT.com

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Lecture 25
Matrix Operations
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Matrix Operations
Matrix Operations - Adding, Subtracting, and Multiplying by a constant for matrices is discussed. For more free math videos, visit http://PatrickJMT.com!
Lecture 26
Orthogonal Projections - Scalar and Vector Projections
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Orthogonal Projections - Scalar and Vector Projections
Orthogonal Projections - Scalar and Vector Projections. In this video, we look at the idea of a scalar and vector projection of one vector onto another.
Lecture 27
An Introduction to the Dot Product
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An Introduction to the Dot Product
An 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.
Lecture 28
Sketching Sums and Differences of Vectors
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Sketching Sums and Differences of Vectors
Sketching 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.
Lecture 29
Word Problems Involving Velocity or Other Forces (Vectors), Ex 3.
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Word Problems Involving Velocity or Other Forces (Vectors), Ex 3.
Word 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.
Lecture 30
Word Problems Involving Velocity or Other Forces (Vectors), Ex 2
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Word Problems Involving Velocity or Other Forces (Vectors), Ex 2
Word 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!)
Lecture 31
Word Problems Involving Velocity or Other Forces (Vectors), Ex 1
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Word Problems Involving Velocity or Other Forces (Vectors), Ex 1
Word Problems Involving Velocity or Other Forces (Vectors), Ex 1. In this problem we do a word problem involving the bearing (direction) of a boat.
Lecture 32
Finding a Unit Vector, Ex 2
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Finding a Unit Vector, Ex 2
Finding a Unit Vector, Ex 2. In this video we find a unit vector associated with a given vector.
Lecture 33
Finding a Unit Vector, Ex 1
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Finding a Unit Vector, Ex 1
Finding 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!).
Lecture 34
Finding the Components of a Vector, Ex 2
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Finding the Components of a Vector, Ex 2
Finding 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.
Lecture 35
Finding the Components of a Vector, Ex 1
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Finding the Components of a Vector, Ex 1
Finding 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.
Lecture 36
Vector Addition and Scalar Multiplication, Example 2
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Vector Addition and Scalar Multiplication, Example 2
Vector 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!).
Lecture 37
Vector Addition and Scalar Multiplication, Example 1
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Vector Addition and Scalar Multiplication, Example 1
Vector 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).
Lecture 38
Magnitude and Direction of a Vector, Example 3
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Magnitude and Direction of a Vector, Example 3
Magnitude and Direction of a Vector, Example 3. Here we find the magnitude (length) of one last vector and find the angle associated with them.
Lecture 39
Magnitude and Direction of a Vector, Example 2
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Magnitude and Direction of a Vector, Example 2
Magnitude and Direction of a Vector, Example 2. Here we find the magnitude (length) of some vectors and find the angle associated with them.
Lecture 40
Magnitude and Direction of a Vector, Example 1
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Magnitude and Direction of a Vector, Example 1
Magnitude and Direction of a Vector, Example 1. Here we find the magnitude (length) of some vectors and find the angle associated with them.
Lecture 41
When Are Two Vectors Considered to Be the Same?
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When Are Two Vectors Considered to Be the Same?
When are two vectors considered to be the same?
Lecture 42
An Introduction to Vectors, Part 1
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An Introduction to Vectors, Part 1
An introduction to vectors: magnitude, direction, length, component form are all discussed.
Lecture 43
Finding the Vector Equation of a Line
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Finding the Vector Equation of a Line
Finding 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.
For more free math videos, visit http://PatrickJMT.com
Lecture 44
Vector Basics - Algebraic Representations Part 2
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Vector Basics - Algebraic Representations Part 2
Vector Basics - Components, adding vectors algebraically and multiplying by a constant. PART 2 of the video that got cut off!!
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Lecture 45
Vector Basics - Algebraic Representations
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Vector Basics - Algebraic Representations
Vector Basics - Components, adding vectors algebraically and multiplying by a constant.
For more free math videos, visit http://PatrickJMT.com
Lecture 46
Vector Basics - Drawing Vectors/ Vector Addition
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Vector Basics - Drawing Vectors/ Vector Addition
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Vector 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.
For more free math videos, visit http://PatrickJMT.com
Lecture 47
Vectors - The Dot Product
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Vectors - The Dot Product
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Vectors - 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.
Lecture 48
Vectors - Finding Magnitude or Length
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Vectors - Finding Magnitude or Length
Vectors - Finding Magnitude or Length. I give the formula, and do a couple examples of finding the magitude, or length, or a vector. Nothing heavy!
For more free videos visit http://PatrickJMT.com
Lecture 49
Linear Independence and Linear Dependence, Ex 2
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Linear Independence and Linear Dependence, Ex 2
Linear 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.
Lecture 50
Linear Independence and Linear Dependence, Ex 1
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Linear Independence and Linear Dependence, Ex 1
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Linear 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.
Lecture 51
Homogeneous Systems of Linear Equations - Trivial and Nontrivial Solutions, Part 2
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Homogeneous Systems of Linear Equations - Trivial and Nontrivial Solutions, Part 2
Homogeneous 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.
Lecture 52
Homogeneous Systems of Linear Equations - Trivial and Nontrivial Solutions, Part 1
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Homogeneous Systems of Linear Equations - Trivial and Nontrivial Solutions, Part 1
Homogeneous 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.
Lecture 53
Useful Things to Remember About Linearly Independent Vectors
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Useful Things to Remember About Linearly Independent Vectors
Useful 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!
Lecture 54
Basis for a Set of Vectors
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Basis for a Set of Vectors
Basis 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.
Lecture 55
Useful Things to Remember About Linearly Independent Vectors
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Useful Things to Remember About Linearly Independent Vectors
Useful 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!
Lecture 56
Procedure to Find a Basis for a Set of Vectors
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Procedure to Find a Basis for a Set of Vectors
Procedure 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!
Lecture 57
Linear Transformations , Example 1, Part 2 of 2
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Linear Transformations , Example 1, Part 2 of 2
Linear 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.
Lecture 58
Linear Transformations , Example 1, Part 1 of 2
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Linear Transformations , Example 1, Part 1 of 2
Linear 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.