  # Complete Quick Lessons on Linear Algebra

## Video Lectures

Displaying all 58 video lectures.
 Lecture 1 Play Video The Span of a Set of VectorsNeed a LIVE tutor to help answer a question? Check out the people at http://www.tutor.com/signup?AdDist=1&ExAdId=90fddaff-89aa-4a... for a FREE 30 minute session! 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 Play Video Determinants to Find the Area of a PolygonDeterminants 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 Play Video Determinants to Find the Area of a TriangleDeterminants 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 Play Video Solving a 3 x 3 System of Equations Using the InverseSolving 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 Play Video Determinant of a 2 x 2 Matrix - A Few Basic QuestionsDeterminant 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 Play Video Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors - Example 3Finding 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 Play Video Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors - Example 2Finding 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 Play Video Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors - Example 1Need a LIVE tutor to help answer a question? Check out the people at http://www.tutor.com/signup?AdDist=1&ExAdId=90fddaff-89aa-4a... for a FREE 30 minute session! 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 Play Video Cramer's Rule to Solve a System of 3 Linear Equations - Example 2Cramer's Rule to Solve a System of 3 Linear Equations - Example 2 Lecture 10 Play Video Cramer's Rule to Solve a System of 3 Linear Equations - Example 1Cramer's Rule to Solve a System of 3 Linear Equations - Example 1 Lecture 11 Play Video Using Gauss-Jordan to Solve a System of Three Linear Equations - Example 2Using Gauss-Jordan to Solve a System of Three Linear Equations - Example 2 Lecture 12 Play Video Using Gauss-Jordan to Solve a System of Three Linear Equations - Example 1Need a LIVE tutor to help answer a question? Check out the people at http://www.tutor.com/signup?AdDist=1&ExAdId=90fddaff-89aa-4a... for a FREE 30 minute session! Using Gauss-Jordan to Solve a System of Three Linear Equations - Example 1 Lecture 13 Play Video Solving a Dependent System of Linear Equations involving 3 VariablesSolving a Dependent System of Linear Equations involving 3 Variables Lecture 14 Play Video Systems of Linear Equations - Inconsistent Systems Using Elimination by Addition - Example 3Systems of Linear Equations - Inconsistent Systems Using Elimination by Addition - Example 3 Lecture 15 Play Video Systems of Linear Equations - Inconsistent Systems Using Elimination by Addition - Example 2Systems of Linear Equations - Inconsistent Systems Using Elimination by Addition - Example 2 Lecture 16 Play Video Systems of Linear Equations - Inconsistent Systems Using Elimination by Addition - Example 1Systems of Linear Equations - Inconsistent Systems Using Elimination by Addition - Example 1 Lecture 17 Play Video Solving a System of Equations Involving 3 Variables Using Elimination by Addition - Example 3Solving 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 Play Video Solving a System of Equations Involving 3 Variables Using Elimination by Addition - Example 2Solving 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 Play Video Solving a System of Equations Involving 3 Variables Using Elimination by Addition - Example 1Solving 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 Play Video Finding the Determinant of a 3 x 3 matrixNeed a LIVE tutor to help answer a question? Check out the people at http://www.tutor.com/signup?AdDist=1&ExAdId=90fddaff-89aa-4a... for a FREE 30 minute session! 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 Play Video Row Reducing a Matrix - Systems of Linear Equations - Part 2Visit : http://bit.ly/pTquLB for your 14 day free trial at Thinkwell! Videos, Quizzes, Tests and More! 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 Austin Math Tutor, Austin Math Tutoring, Austin Algebra Tutor, Austin Calculus Tutor Lecture 22 Play Video Row Reducing a Matrix - Systems of Linear Equations - Part 1Row 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 Austin Math Tutor, Austin Math Tutoring, Austin Algebra Tutor, Austin Calculus Tutor Lecture 23 Play Video Solving Systems of Equations Using Elimination By AdditionSolving 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 Play Video Multiplying Matrices - Example 1Need a LIVE tutor to help answer a question? Check out the people at http://www.tutor.com/signup?AdDist=1&ExAdId=90fddaff-89aa-4a... for a FREE 30 minute session! Multiplying Matrices - Two examples of multiplying a matrix by another matrix are shown. For more free math videos, visit http://PatrickJMT.com Austin Math Tutor, Austin Math Tutoring, Austin Algebra Tutor, Austin Calculus Tutor Austin Math Tutor, Austin Math Tutoring, Austin Algebra Tutor, Austin Calculus Tutor Lecture 25 Play Video Matrix OperationsMatrix Operations - Adding, Subtracting, and Multiplying by a constant for matrices is discussed. For more free math videos, visit http://PatrickJMT.com! Lecture 26 Play Video Orthogonal Projections - Scalar and Vector ProjectionsOrthogonal 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 Play Video An Introduction to the Dot ProductAn 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 Play Video Sketching Sums and Differences of VectorsSketching 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 Play Video 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 Play Video Word Problems Involving Velocity or Other Forces (Vectors), Ex 2Word 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 Play Video Word Problems Involving Velocity or Other Forces (Vectors), Ex 1Word 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 Play Video Finding a Unit Vector, Ex 2Finding a Unit Vector, Ex 2. In this video we find a unit vector associated with a given vector. Lecture 33 Play Video Finding a Unit Vector, Ex 1Finding 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 Play Video Finding the Components of a Vector, Ex 2Finding 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 Play Video Finding the Components of a Vector, Ex 1Finding 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 Play Video Vector Addition and Scalar Multiplication, Example 2Vector 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 Play Video Vector Addition and Scalar Multiplication, Example 1Vector 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 Play Video Magnitude and Direction of a Vector, Example 3Magnitude 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 Play Video Magnitude and Direction of a Vector, Example 2Magnitude 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 Play Video Magnitude and Direction of a Vector, Example 1Magnitude 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 Play Video When Are Two Vectors Considered to Be the Same?When are two vectors considered to be the same? Lecture 42 Play Video An Introduction to Vectors, Part 1An introduction to vectors: magnitude, direction, length, component form are all discussed. Lecture 43 Play Video Finding the Vector Equation of a LineFinding 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 Play Video Vector Basics - Algebraic Representations Part 2Vector Basics - Components, adding vectors algebraically and multiplying by a constant. PART 2 of the video that got cut off!! For more free math videos, visit http://JustMathTutoring.com Lecture 45 Play Video Vector Basics - Algebraic RepresentationsVector Basics - Components, adding vectors algebraically and multiplying by a constant. For more free math videos, visit http://PatrickJMT.com Lecture 46 Play Video Vector Basics - Drawing Vectors/ Vector AdditionNeed a LIVE tutor to help answer a question? Check out the people at http://www.tutor.com/signup?AdDist=1&ExAdId=90fddaff-89aa-4a... for a FREE 30 minute session! 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 Play Video Vectors - The Dot ProductFor more FREE math videos, visit http://PatrickJMT.com !! 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 Play Video Vectors - Finding Magnitude or LengthVectors - 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 Play Video Linear Independence and Linear Dependence, Ex 2Linear 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 Play Video Linear Independence and Linear Dependence, Ex 1Need a LIVE tutor to help answer a question? Check out the people at http://www.tutor.com/signup?AdDist=1&ExAdId=90fddaff-89aa-4a... for a FREE 30 minute session! 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 Play Video Homogeneous Systems of Linear Equations - Trivial and Nontrivial Solutions, Part 2Homogeneous 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 Play Video Homogeneous Systems of Linear Equations - Trivial and Nontrivial Solutions, Part 1Homogeneous 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 Play Video Useful Things to Remember About Linearly Independent VectorsUseful 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 Play Video Basis for a Set of VectorsBasis 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 Play Video Useful Things to Remember About Linearly Independent VectorsUseful 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 Play Video Procedure to Find a Basis for a Set of VectorsProcedure 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 Play Video Linear Transformations , Example 1, Part 2 of 2Linear 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 Play Video Linear Transformations , Example 1, Part 1 of 2Linear 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.