Linear Algebra

Study of vectors, matrices, and linear transformations.

Vectors and Their OperationsMatrices and Matrix ArithmeticLinear Transformations
Determinants and InversesEigenvalues and EigenvectorsVector Spaces and Subspaces
Computer Graphics and AnimationData Science and Machine LearningRobotics and Engineering
Breaking Down Word ProblemsChecking Your Solutions with InversesVisualizing Problems to Find Solutions
Vectors and Their Op...Matrices and Matrix ...Linear Transformatio...Determinants and Inv...Eigenvalues and Eige...Vector Spaces and Su...Computer Graphics an...Data Science and Mac...Robotics and Enginee...Breaking Down Word P...Checking Your Soluti...Visualizing Problems...
Practical Applications

Robotics and Engineering

Making Robots Move

Robots use vectors and matrices to figure out how to move arms, wheels, or sensors. Each joint or part is described with coordinates, and matrices help calculate the right positions.

  • Kinematics: Using matrices to calculate the movement of robot arms.
  • Control Systems: Linear algebra helps design stable and efficient robots.

Real-World Impact

From self-driving cars to manufacturing robots, linear algebra makes modern engineering possible.

Practice

  • Use a transformation matrix to move a robot's arm to a new position.
  • Analyze the stability of a robot's movement system using matrices.

Examples

  • Robot arm paths are calculated using rotation and translation matrices.

  • Engineering simulations use matrices to predict stresses and strains.

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Breaking Down Word Problems