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

Checking Your Solutions with Inverses

Double-Check Your Work

If you've solved a system using matrices, use the matrix inverse to check your solution. Multiply your answer (vector) by the original matrix and see if you get the original constants. If you do, your solution is correct!

Steps

  • Solve the system using matrices.
  • Multiply the matrix by your solution vector.
  • Compare the result to the original right-hand side.

Examples

  • Multiplying the solution vector by the coefficient matrix to verify your answer.

  • Using the identity matrix to check that an inverse is correct.

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Visualizing Problems to Find Solutions