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
What this standard means
Students need to decide whether a square matrix has an inverse, find that inverse when it exists, and use it to solve a linear system written as AX = B. They should connect the matrix setup to the original equations, not just press buttons.
Mastery looks like setting up A, X, and B correctly, checking that the inverse exists, computing or using technology accurately, and interpreting the solution. Students often mix up row and column order, forget that only square coefficient matrices can have inverses, or treat a calculator output as final without checking in the equations.
Ways to teach it
- Use colored cards for coefficients, variables, and constants, then have students build A, X, and B from a three-equation system.
- Ask students to explain why solving AX = B gives X = A inverse times B, using one simple 2 by 2 example.
- Give one 2 by 2 system and ask students to find the inverse, solve, and check the ordered pair in both equations.
- Show how traffic flow at three connected intersections can be modeled with a matrix system and solved using a calculator.
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Related standards
- CCSS.Math.Content.HSN-VM.C.8
(+) Add, subtract, and multiply matrices of appropriate dimensions.
- 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.HSA-REI.C.8
(+) Represent a system of linear equations as a single matrix equation in a vector variable.
- 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.