Product Review

Linear Algebra is a course that is usually taken by Sophomore or Junior students in Engineering, Science, and Mathematics. Learn Linear Algebra with step-by-step example problems!

Disk 1
Sect 1: Matrices, Elements, and Transpose
Sect 2: n-Tuples and Matrix Arithmetic, Part 1
Sect 3: n-Tuples and Matrix Arithmetic, Part 2
Sect 4: Matrix Multiplication
Sect 5: The Vector Dot Product
Sect 6: Special Matrices
Sect 7: The Norm of a Vector
Sect 8: Unit Vectors in any Direction
Sect 9: Vector Addition and Triangle Inequalities

Disk 2
Sect 10: Orthogonal and Orthonormal Vectors
Sect 11: Solve Systems of Equations with Row Reduction, Part 1
Sect 12: Solve Systems of Equations with Row Reduction, Part 2
Sect 13: Solve Systems of Equations with Row Reduction, Part 3
Sect 14: Solve Systems of Equations with Row Reduction, Part 4
Sect 15: Solve Systems of Equations with Row Reduction, Part 5
Sect 16: Homogeneous Systems of Equations
Sect 17: Inverse of a 2x2 Matrix
Sect 18: Inverse of a 3x3 and Larger Matrix
Sect 19: Solve Systems of Equations with Inverse Matrices

This course begins with a review of matrices and then explores the concept of a vector as a matrix. Next, we learn how to add and subtract matrices and vectors and how to multiply them by a scalar quantity.

Next, we discuss the norm (magnitude) of a vector and learn about the associated triangle inequalities. Then, we spend a great deal of time learning how to solve systems of equations by matrix row reduction operations, including homogeneous systems. We spend a good deal of time discussing how to handle systems with an infinite set of solutions and how to properly solve for and write down the answer.

Finally, we introduce the concept of a matrix inverse and learn how to calculate an inverse of any size. We also learn how to solve a system of equations using the matrix inverse.

The easiest way to learn this material is through step-by-step video lessons!