Lesson Plan

Write a system of two linear equations as the matrix equation AX = B, identifying the coefficient, variable, and constant matrices, and verify the rewrite by expanding AX

Compute the determinant of a 2×2 coefficient matrix and interpret a nonzero value as guaranteeing a unique solution

Apply the 2×2 inverse formula (recalled from act-nq-vecmat-det) to solve a system as X = A⁻¹B

Solve a 2×2 system using Cramer's rule, constructing the column-replacement matrices correctly

Interpret a zero determinant as the system having no unique solution (none or infinitely many)

Decide when the matrix route is the efficient choice on an ACT item, 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