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...
Study Strategies

Visualizing Problems to Find Solutions

Picture It!

Many linear algebra problems become easier when you draw them. Sketch vectors, matrices as grids, or transformations as movements on a plane. Seeing the problem visually helps you understand what’s really happening.

Steps

  • Draw the vectors or matrices involved.
  • Use arrows for vectors and boxes for matrices.
  • Mark transformations like rotations or reflections.

Examples

  • Drawing a vector addition problem as arrows on a grid.

  • Sketching a matrix transformation to see how it changes a shape.