Download Commander Day #4 Matrices Lesson plan

Washington County Schools
Commander Day Lesson Plans
2015-16
Commander Day Lessons focus on the review and application of skills that students have previously
learned.
Students will submit a work product or learning log to demonstrate completion of a lesson.
Student work must be submitted no later than two days following the return from the Commander Day.
Content Area: _Algebra 2___________
Grade Level: _10-12_______________
Snow Day Lesson Number: 1 – 2 – 3 – 4 – 5 – 6 – 7 – 8 – 9 - 10
Content Topic:
Matrices spiral review
Standard(s):
N.VM.7 Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a
game are doubled.
N.VM.8 Add, subtract, and multiply matrices of appropriate dimensions.
N.VM.10 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.
N.VM.6 Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence
relationships in a network.
N.VM.8 Add, subtract, and multiply matrices of appropriate dimensions.
N.VM.9 Understand that, unlike multiplication of numbers, matrix multiplication for square matrices
is not a commutative operation, but still satisfies the associative and distributive properties. N.VM.10
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.
N.VM.12 Work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value
of the determinant in terms of area.
Essential Question (Students should be able to answer following the lesson):
 Simplify matrix operations
 What matrix operations are used to solve matrix equations
 How can you use matrix equations to solve systems of equations
Critical Vocabulary (Terminology to be included in the lesson):
Matrix operations
Matrix Determinants
Matrix Inverse
Matrix Equation
Linear System
Learning Activities and Steps (Work students will complete):
Complete the matrices spiral review worksheet
Formulas to use:
Matrix Add/Subtraction: Add/Sub corresponding elements if matrices have same dimensions
𝑒 𝑓
𝑎±𝑒 𝑏±𝑓
𝑎 𝑏
[
]± [
]= [
]
𝑔 ℎ
𝑐±𝑔 𝑑±ℎ
𝑐 𝑑
𝑎 𝑏
𝑎𝑥 𝑏𝑥
Matrix Scalar Multiplication: Use distributive property 𝑥 [
]= [
]
𝑐 𝑑
𝑐𝑥 𝑑𝑥
Matrix Multiplication: 𝑚 × 𝑛 ∙ 𝑛 × 𝑝 = 𝑚 × 𝑝 the number of columns must equal the
number of rows. Multiple the rows of the first matrix by the columns of the second matrix
𝑒 𝑓
𝑎𝑒 + 𝑏𝑔 𝑎𝑓 + 𝑏ℎ
𝑎 𝑏
[
]∙[
]= [
]
𝑐𝑒 + 𝑑𝑔 𝑐𝑓 + 𝑑ℎ
𝑐 𝑑 𝑔 ℎ
𝑎 𝑏
Matrix Determinant: 2x2: |
| = 𝑎𝑑 − 𝑐𝑏
𝑐 𝑑
𝑎 𝑏 𝑐
𝑎 𝑏 𝑐 𝑎 𝑏
3x3: |𝑑 𝑒 𝑓 | = |𝑑 𝑒 𝑓 | 𝑑 𝑒 = (𝑎𝑒𝑖 + 𝑏𝑓𝑔 + 𝑐𝑑ℎ) − (𝑔𝑒𝑐 + ℎ𝑓𝑎 + 𝑖𝑑𝑏)
𝑔 ℎ 𝑖
𝑔 ℎ 𝑖 𝑔 ℎ
−1
1
𝑎 𝑏
𝑑 −𝑏
Matrix Inverse: [
] = 𝑎𝑑−𝑐𝑏 [
]
𝑐 𝑑
−𝑐 𝑎
Matrix Equations: 𝐴𝑋 = 𝐵
𝐴−1 𝐴𝑋 = 𝐵
𝑋 = 𝐴−1 𝐵
𝑒
𝑎𝑥 + 𝑏𝑦 = 𝑒
𝑎 𝑏 𝑥
Linear System:
[
] [𝑦] = [𝑓]
𝑐𝑥 + 𝑑𝑦 = 𝑓
𝑐 𝑑
𝑥
𝑎 𝑏 −1 𝑒
[𝑦 ] = [
] [𝑓]
𝑐 𝑑
Technology Activity Option (Students may choose to complete in place of other activity):
30 min of Cert
www.certforschools.com
username: [email protected]
password: wchs2015
Necessary Resources:
Matrices review worksheet