- standard
Perform operations on matrices and use matrices in applications
- 9th - 12th Grade
- Michigan State Math Standards
- Number and Quantity: Vector and Matrix Quantities
(+) Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformation…
- standard
Perform operations on matrices and use matrices in applications
- 9th - 12th Grade
- Michigan State Math Standards
- Number and Quantity: Vector and Matrix Quantities
(+) 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 de…
- standard
Perform operations on vectors
- 9th - 12th Grade
- Michigan State Math Standards
- Number and Quantity: Vector and Matrix Quantities
(+) 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 a…
- standard
Perform operations on vectors
- 9th - 12th Grade
- Michigan State Math Standards
- Number and Quantity: Vector and Matrix Quantities
(+) Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., …
- standard
Perform operations on vectors
- 9th - 12th Grade
- Michigan State Math Standards
- Number and Quantity: Vector and Matrix Quantities
(+) Perform operations on vectors. Multiply a vector by a scalar.
- standard
Perform operations on vectors
- 9th - 12th Grade
- Michigan State Math Standards
- Number and Quantity: Vector and Matrix Quantities
(+) 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 directi…
- standard
Perform operations on vectors
- 9th - 12th Grade
- Michigan State Math Standards
- Number and Quantity: Vector and Matrix Quantities
(+) Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
- standard
Perform operations on vectors
- 9th - 12th Grade
- Michigan State Math Standards
- Number and Quantity: Vector and Matrix Quantities
(+) 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 th…
- standard
Perform operations on vectors
- 9th - 12th Grade
- Michigan State Math Standards
- Number and Quantity: Vector and Matrix Quantities
(+) Add and subtract vectors.
- standard
Represent and model with vector quantities.
- 9th - 12th Grade
- Michigan State Math Standards
- Number and Quantity: Vector and Matrix Quantities
(+) Solve problems involving velocity and other quantities that can be represented by vectors.
- standard
Represent and model with vector quantities.
- 9th - 12th Grade
- Michigan State Math Standards
- Number and Quantity: Vector and Matrix Quantities
(+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
- standard
Represent and model with vector quantities.
- 9th - 12th Grade
- Michigan State Math Standards
- Number and Quantity: Vector and Matrix Quantities
(+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for …
- standard
Use complex numbers in polynomial identities and equations
- 9th - 12th Grade
- Michigan State Math Standards
- Number and Quantity: The Complex Number System
(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
- standard
Use complex numbers in polynomial identities and equations
- 9th - 12th Grade
- Michigan State Math Standards
- Number and Quantity: The Complex Number System
(+) Extend polynomial identities to the complex numbers. For example, rewrite x^2 + 4 as (x + 2i)(x – 2i).