Curriculum placement
Precalculus. This describes the skill, not a learner estimate.
A system written as a matrix equation
Represent systems as matrix equations and solve using inverses where possible
Problem types
- Linear systems as matrix equations
- Write a system as one matrix equation
- Read a matrix equation as a system
Builds on
- Inverse of a matrix
- Systems of linear equations
- Data arranged in a matrix · Earlier idea
Data stored in a matrix are combined by multiplying matrices, and unknowns are found by solving the matrix system.
- Systems that model two constraints · Earlier idea
A system from a situation is written as a matrix equation whose solution is found with an inverse.
- Why elimination keeps the same solutions · Useful idea
Adding multiples of one equation to another in elimination is the row operation used to solve systems with matrices.
- Linear equations with letter coefficients · Useful idea
Whether a parameter gives one, none or infinitely many solutions is decided by the same conditions that decide matrix systems.
Leads to
- Matrices as transformations of the plane · See it applied
Solving AX = B asks which point the matrix A sends to B, so the inverse undoes the transformation.
- Velocity and force as vectors · See it applied
Finding components of vectors that add to a given resultant solves a linear system.
- Reading slope and intercept in context · See it applied
Fitting a line through data solves a linear system for the slope and intercept.
Related skills
- Solving a linear and a nonlinear equation together · Shared foundations
Open the interactive map to explore lessons and skill connections.