
Discover how to maximize learning in this course by using notes with formulas, video walkthroughs, and quizzes, plus access step-by-step solutions and extra practice workbooks for each section.
Learn how to determine whether a linear system has one, none, or infinitely many solutions using Gauss Jordan elimination, identifying pivot and free variables in the reduced row echelon form.
Learn to add and subtract matrices with matching dimensions, using corresponding entries; note that addition is commutative and associative, while subtraction is not, then solve matrix equations.
Explore vectors as directional quantities defined by length and direction, distinct from matrices. Learn vector arithmetic, linear combinations, linear independence, and the ideas of spaces and basis vectors.
the span of a vector set is always a subspace, closed under addition and scalar multiplication, and contains the zero vector.
Define basis as a spanning, linearly independent vector set that defines a subspace, with two vectors in R2 forming a basis for that space.
Explore the Cauchy–Schwarz inequality, linking the absolute dot product to the product of vector lengths. Learn when equality occurs for scalar multiples, and test linear independence versus dependence with examples.
Define planes in three-dimensional space from a normal vector and a vector in the plane. Derive the plane's equation Ax+By+Cz=D using a point and the normal, via the dot product.
Explore how matrix-vector products reveal the four fundamental subspaces—null space, column space, row space, and left null space—and solve for the null and column spaces.
Compute the null space of a 3 by 4 matrix by reducing to reduced row echelon form, identifying pivot and free columns, and expressing the solution as the span of [0,1,0,0] and [-1,0,0,1].
Explores how a transformation maps vectors from subset a to subset b, and defines the image, the preimage, and the kernel as all vectors mapping to the zero vector.
Explore projecting onto a line as a linear transformation by constructing a projection matrix A for the line L spanned by (2,1) and using A to project onto L.
Solve a linear system by multiplying the inverse of the coefficient matrix by the right-hand side vector. Compute the inverse via determinant formula or augmented form, then get x and y.
Determinants help find the area of transformed figures by treating matrix columns as adjacent sides of a parallelogram, with area scaled by the absolute value of the transformation's determinant.
Define the transpose by swapping rows and columns, then show how to calculate it. Explore how determinants and the four fundamental sub spaces relate between a matrix and its transpose.
Master how transposes interact with products, sums, and inverses, using the key rules (AB)^T = B^T A^T, (A+B)^T = A^T + B^T, and (A^T)^{-1} = (A^{-1})^T.
HOW BECOME A LINEAR ALGEBRA MASTER IS SET UP TO MAKE COMPLICATED MATH EASY:
This 247-lesson course includes video and text explanations of everything from Linear Algebra, and it includes 69 quizzes (with solutions!) and an additional 12 workbooks with extra practice problems, to help you test your understanding along the way. Become a Linear Algebra Master is organized into the following sections:
Operations on one matrix, including solving linear systems, and Gauss-Jordan elimination
Operations on two matrices, including matrix multiplication and elimination matrices
Matrices as vectors, including linear combinations and span, linear independence, and subspaces
Dot products and cross products, including the Cauchy-Schwarz and vector triangle inequalities
Matrix-vector products, including the null and column spaces, and solving Ax=b
Transformations, including linear transformations, projections, and composition of transformations
Inverses, including invertible and singular matrices, and solving systems with inverse matrices
Determinants, including upper and lower triangular matrices, and Cramer's rule
Transposes, including their determinants, and the null (left null) and column (row) spaces of the transpose
Orthogonality and change of basis, including orthogonal complements, projections onto a subspace, least squares, and changing the basis
Orthonormal bases and Gram-Schmidt, including definition of the orthonormal basis, and converting to an orthonormal basis with the Gram-Schmidt process
Eigenvalues and Eigenvectors, including finding eigenvalues and their associate eigenvectors and eigenspaces, and eigen in three dimensions
AND HERE'S WHAT YOU GET INSIDE OF EVERY SECTION:
Videos: Watch over my shoulder as I solve problems for every single math issue you’ll encounter in class. We start from the beginning... I explain the problem setup and why I set it up that way, the steps I take and why I take them, how to work through the yucky, fuzzy middle parts, and how to simplify the answer when you get it.
Notes: The notes section of each lesson is where you find the most important things to remember. It’s like Cliff Notes for books, but for math. Everything you need to know to pass your class and nothing you don’t.
Quizzes: When you think you’ve got a good grasp on a topic within a course, you can test your knowledge by taking one of the quizzes. If you pass, great! If not, you can review the videos and notes again or ask for help in the Q&A section.
Workbooks: Want even more practice? When you've finished the section, you can review everything you've learned by working through the bonus workbook. The workbooks include tons of extra practice problems, so they're a great way to solidify what you just learned in that section.
HERE'S WHAT SOME STUDENTS OF BECOME A LINEAR ALGEBRA MASTER HAVE TOLD ME:
“Another fantastic course. Provides an academic foundation of linear algebra to prepare for applied or programming-based courses.” - Christopher C.
“I have no words to thank Krista for this amazing course, I was really overwhelmed because I had to take a test for a class I couldn't attend and I didn't know anything about linear algebra and surprisingly this course was what I needed, reading the notes before watching the video helped to understand by myself and when I was lost the video content was a great resource, I got a 9 out of 10 in the test, so I highly recommend to take this course, Krista is such a good teacher.” - Alan M.
“I started out as a math major in college, and dropped my major during linear algebra. I wish I had this class and this instructor in college. I might have stuck with my major.” - Eric L.
“Notes are great, explanations are clear and starting from the beginning. Terrific so far.” - Phil T.
“Very clear and has not skipped any steps. If the rest of the course is like this, I will pass my class with no problem.” - Brandon P.
“Really well structured and well explained, and there are plenty of exercises to reinforce the knowledge.” - Ashfaque C.
YOU'LL ALSO GET:
Lifetime access to Become a Linear Algebra Master
Friendly support in the Q&A section
Udemy Certificate of Completion available for download
30-day money back guarantee
Enroll today!
I can't wait for you to get started on mastering Linear Algebra.
- Krista :)