The student will create, manipulate, and solve systems of equations and matrices and apply them to programming arrays.
Systems of Equations and Matrices
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Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation but still satisfies the associative and distributive properties
Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers; the determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse
Work with 2 × 2 matrices as transformations of the plane and interpret the absolute value of the determinant in terms of area
Represent a system of linear equations as a single matrix equation in a vector variable
Find the inverse of a matrix if it exists and use it to solve systems of linear equations; use technology for matrices of dimension 3 × 3 or greater