MGSE9-12.N.VM.7: Multiply matrices by scalars to produce new matrices.

MGSE9-12.N.VM.8: Add, subtract, and multiply matrices of appropriate dimensions.

MGSE9-12.N.VM.10:Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.

MGSE9-12.N.VM.9: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.

MGSE9-12.N.VM.10:Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.

MGSE9-12.N.VM.9: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.

MGSE9-12.N.VM.12:Work with 2 X 2 matrices as transformations of the plane and interpret the absolute value of the determinant in terms of area.

MGSE9-12.N.VM.12:Represent a system of linear equations as a single matrix equation in a vector variable.

MGSE9-12.A.REI.9:Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).

MGSE9-12.N.VM.6:Use matrices to represent and manipulate data, e.g., transformations of vectors.

MGSE9-12.N.VM.7: Multiply matrices by scalars to produce new matrices.

MGSE9-12.N.VM.8:Add, subtract, and multiply matrices of appropriate dimensions.

MGSE9-12.N.VM.6:Use matrices to represent and manipulate data, e.g., transformations of vectors.

MGSE9-12.N.VM.7: Multiply matrices by scalars to produce new matrices.

MGSE9-12.N.VM.8:Add, subtract, and multiply matrices of appropriate dimensions.

MGSE9-12.N.VM.12:Work with 2 X 2 matrices as transformations of the plane and interpret the absolute value of the determinant in terms of area.

MGSE9-12.N.VM.1: Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).

MGSE9-12.N.VM.2 Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

MGSE9-12.N.VM.3: Solve problems involving velocity and other quantities that can be represented by vectors.

MGSE9-12.N.VM.4 :Add and subtract vectors.

MGSE9-12.N.VM4a: Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.

MGSE9-12.N.VM4b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

MGSE9-12.N.VM4c: Understand vector subtraction v – w as v + (–w), where (–w) is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.

MGSE9-12.N.VM.5 :Multiply a vector by a scalar

MGSE9-12.N.VM.5a: Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).

MGSE9-12.N.VM.5b: 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).

MGSE9-12.N.VM.11 :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.