CCSS.Math.Content.HSA-REI.C.9
The Standard
(+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students write a linear system as a matrix equation and determine whether the coefficient matrix has an inverse. They use the inverse to calculate the solution, using technology for matrices of size 3 by 3 or larger.
What Mastery Looks Like
- Students can find a 2 by 2 inverse, identify when no inverse exists, and solve for the variable matrix. They use matrix software for larger systems and verify the solution in the original equations.
Common Misconceptions
- Students may take the reciprocal of each matrix entry instead of finding the inverse. They may reverse multiplication order or assume every square matrix is invertible. A zero determinant means there is no inverse and no unique solution.
How to Assess It
- Exit ticket: Write 2x + y = 7 and x - y = 2 as AX = B, find A⁻¹, solve, and verify by substitution.
Lesson moves
Ways to Teach It
Give groups coefficient, inverse, and identity matrix cards, then have them multiply to match valid inverse pairs and flag singular matrices.
Ask students to write why a zero determinant prevents the inverse method from producing one unique solution.
Run a relay where teams solve 2 by 2 systems with inverses and earn points only after checking AX = B.
Model ticket sales with three ticket types, three revenue equations, and a graphing calculator to find the numbers sold.
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Printable HSA-REI.C.9 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSA-REI.C.9, with an answer key for the teacher on its own page. No account needed.
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Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.HSA-REI.C.8
Solving systems with inverses requires first writing the equations as AX = B so the inverse can act on the vector.
- CCSS.Math.Content.HSN-VM.C.8
Matrix multiplication and dimension rules carry into understanding inverses, identity matrices, and multiplying an inverse by a constants vector.
- CCSS.Math.Content.HSN-VM.C.10
Knowing identity matrices and the determinant test helps students decide when an inverse exists before solving systems with it.
Keep exploring
Related Standards
- CCSS.Math.Content.HSF-TF.B.7
(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms...
- CCSS.Math.Content.HSN-VM.C.12
(+) Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.
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