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Washington County Schools Commander Day Lesson Plans 2016-17 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