What the learner will study

• Graphical Solutions of Linear–Nonlinear Systems
• Solving Nonlinear Systems by Substitution
• Polynomial, Rational & Radical Systems
• Matrix Vocabulary, Dimensions & Operations
• Matrix Equations, Row Reduction & Systems
• Determinants, Inverses & Transformation Models

How to support without taking over

• Ask the learner to define inputs, outputs, units, and domain.
• Ask which property or theorem justifies each transformation.
• Request an independent check by substitution, graph, table, or alternate method.
• Encourage correction notes rather than erasing evidence of learning.
• Use the calculator after the mathematical setup is visible.

Evidence to preserve

Keep one worked example, one correction, one application or project artifact, the mastery result, and a reflection explaining growth and next steps.

Applied investigation

Nonlinear System & Matrix Decision Laboratory asks the learner to define a real question, construct mathematics, validate results, state uncertainty, and communicate a defensible conclusion.