This collection of exercises is designed to provide a framework for discussion in a junior level linear algebra class such as the one I have conducted fairly regularly at Portland State University.

Linear algebra questions with solutions and detailed explanations on matrices , spaces, subspaces and vectors , determinants , systems of linear equations and online linear algebra calculators are included.

I have never formally written solutions to these problems. However, I have frequently used similar problems in Homework and Exams in my own linear algebra courses – in which I often have written …

Learn linear algebra—vectors, matrices, transformations, and more.

OCW is open and available to the world and is a permanent MIT activity.

Looking for interactive exercises on Linear Algebra? Engage your students and help them grasp the concept of Linear Algebra by offering immediate feedback.

W is linear and a bijection. Then we have an inverse map L¡1 which satis ̄es L ± L¡1 = IW and L¡1 ± L = IV . In order for this inverse map to be allowable as K we need to check that it is linear. Select ®1; ®2 …

Solving Systems of Linear Equations by Graphing Given two linear equations in standard form, solve the system of equations by graphing to find the intersection point.

There are methods for solving linear systems other than Gauss' method. One often taught in high school is to solve one of the equations for a variable, then substitute the resulting expression into other …

Prepare for your linear algebra exam with clear video lessons, exam-style practice problems, and a full review playlist. Master key topics with step-by-step explanations and practice you can trust.