Key Concepts & Glossary
Key Equations
Identity matrix for a matrix | |
Identity matrix for a matrix | |
Multiplicative inverse of a matrix |
Key Concepts
- An identity matrix has the property .
- An invertible matrix has the property .
- Use matrix multiplication and the identity to find the inverse of a matrix.
- The multiplicative inverse can be found using a formula.
- Another method of finding the inverse is by augmenting with the identity.
- We can augment a matrix with the identity on the right and use row operations to turn the original matrix into the identity, and the matrix on the right becomes the inverse.
- Write the system of equations as , and multiply both sides by the inverse of .
- We can also use a calculator to solve a system of equations with matrix inverses.
Glossary
- identity matrix
- a square matrix containing ones down the main diagonal and zeros everywhere else; it acts as a 1 in matrix algebra
- multiplicative inverse of a matrix
- a matrix that, when multiplied by the original, equals the identity matrix
Licenses & Attributions
CC licensed content, Specific attribution
- Precalculus. Provided by: OpenStax Authored by: OpenStax College. Located at: https://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1/Preface. License: CC BY: Attribution.