Dearborn Educational Curriculum

Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).

Grade levels
09, 10, 11, 12

(+) 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.

Grade levels
09, 10, 11, 12

(+) Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.

Grade levels
09, 10, 11, 12

(+) Work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.

Grade levels
09, 10, 11, 12

(+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.

Grade levels
09, 10, 11, 12

(+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.

Grade levels
09, 10, 11, 12

(+) Add, subtract, and multiply matrices of appropriate dimensions.

Grade levels
09, 10, 11, 12

(+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.

Grade levels
09, 10, 11, 12