Lesson Plan

Solve a system of two linear equations by X = A⁻¹B (with the 2×2 inverse formula recalled from act-nq-vecmat-det) or by Cramer's rule (column replacement), after writing it as the matrix equation AX = B

Write a system as AX = B, identifying the coefficient, variable, and constant matrices, and verify the rewrite by expanding AX

Compute the determinant of the 2×2 coefficient matrix and read its verdict: nonzero means a unique solution; zero means no unique solution (none or infinitely many)

Decide when the matrix route is the efficient choice, and when it is not

N 406. Add two matrices that have whole number entries N 505. Add and subtract matrices that have integer entries N 607. Use relations involving addition, subtraction, and scalar multiplication of vectors and of matrices N 705. Multiply matrices N 706. Apply properties of matrices and properties of matrices as a number system Note: A matrix as a representation of data is treated here as a basic table. A 604. Solve systems of two linear equations