4.1 An Introduction to Matrices Need Graph Paper

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4.1 An Introduction to MatricesNeed Graph Paper!

• Objective
• To perform scalar multiplication on a matrix.
• To solve matrices for variables.
• To solve problems using matrix logic.

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• Vocabulary
• Matrix- a rectangular array of variables or
  constants in horizontal rows and vertical columns
• Element- each value in the matrix
• Dimensions- each matrix is made up by rows and
  columns.
• Transformations- functions that map points of a
  shape onto its image
• Dilation- a geometric figure is enlarged or
  reduced
• Scalar multiplication- multiply a matrix by a
  constant

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• Naming the dimensions of the matrix

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• Scalar Multiplication of a Matrix
• 1) 2)

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• Solve for the variables
• 3) 4)

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• 5) Jim, Mario, and Mike are married to Shana,
  Kelly, and Lisa. Use these clues to find out who
  is married to whom.
• a. Mario is Kellys brother and lives in Florida
  with his wife.
• b. Mike is shorter than Lisas husband.
• c. Mike works at a bank.
• Shana and her husband live in Kentucky.
• Kelly and her husband work in their candy store.

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• 6) Triangle ABC has vertices A(1, -4), B(2, 3),
  and C(-2, -1). Enlarge Triangle ABC so that its
  perimeter is twice the original perimeter. What
  are the coordinates of triangle ABC? Use
  matrices to solve this problem.

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• 4.1 Assignment
• Page 191 (13-29) odd, 32, 34, 35, 36, 37, 38

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4.1A MatricesGraphing Technology
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• Enter matrix A in a graphing calculator.
• 1)

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• Enter matrix B in a graphing calculator. Then
  find 2A, AB, B AB, the determinant of A and the
  inverse of A.
• 2)

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• 4.1A Assignment
• Page 185 (1-18)

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4.2 Adding and Subtracting MatricesNeed Graph
Paper!

• Objective
• To add and subtract matrices

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• Vocabulary
• Translation- a figure is moved from one location
  to another without changing size, shape, or
  orientation.

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• Determine if you can add or subtract matrices
  and evaluate if possible.
• 1.) 2.)

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• Determine if you can add or subtract matrices
  and evaluate if possible.
• 3.) 4.)

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• 6) Find the coordinate of the vertices of
  quadrilateral QUAD with Q(-2, -3),
  U(-1, 2), A(3, 4), and D(1, -2) if it is moved 3
  units to the right and 1 unit down. Use matrices
  to solve.

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• 4.2 Assignment
• Page 197 (11-19) odd, 23, 25, 26, 27

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4.3 Multiplying MatricesNeed Graph Paper!

• Objective
• To multiply matrices

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• Vocabulary
• Rotation- a figure is moved around a center point

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• When can you add or subtract matrices?

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• When can you multiply matrices?
• a) b)

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• Multiply matrices if possible.
• 1) 2)

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• 3) Quadrilateral ABCD has vertices A(-3, 8),
  B(-2, -1), C(5, -4), and D(3, 6). Find the
  coordinates of the vertices of this quadrilateral
  after it is rotated counterclockwise 90 degrees
  about the origin. Find the rotation matrix.

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• 4.3 Assignment
• Page 202 (18-24), (26-27), 35, 36, 40, 41, 42,
  43, 44, 45, 46

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4.4 Matrices and Determinants

• Objective
• To evaluate the determinant of a 3 x 3 matrix.
• To find the area of a triangle, given the
  coordinates of its vertices.

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• Evaluate by using expansion by minors.
• 1) 2)

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• Evaluate by using diagonals.
• 3) 4)

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• 5) Find the area of the triangle whose vertices
  are located at (3, -4), (5, 4), and (-3, 2) by
  using matrices.

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• 4.4 Assignment
• Page 209 (11-27) odd, 28, 29, 36, 37, 38, 39, 40,
  41, 42

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4.5 Identity and Inverse Matrices

• Objective
• To write the identity matrix for any square
  matrix
• To find the inverse of a 2 x 2 matrix

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• Vocabulary
• Identity Matrix- the matrix that has a value of
  one when you find the determinant of it.

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• Find I so N(I) N.
• 1) 2)

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• 3) 4)

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• 4.5 Assignment
• Page 217 (11-29) odd, 16, 18, 32, 34, 35, 36, 37,
  38, 39

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4.6 Using Matrices to Solve Systems of Equations

• Objective
• To solve systems of linear equations by using
  inverse matrices.

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• Write each system of equations as a matrix
  equation.
• 3x 2y 7 2) 3a 5b 2c 9
• 4x y 8 4a 7b c 3
• 2a c 12

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• Use a matrix equation to solve the system of
  equations.
• 7x 5y 3
• 3x 2y 22

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• Use a matrix equation to solve the system of
  equations.
• 4) 4x 12y 7
• x 6y 9

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• Use a matrix equation to solve the system of
  equations. Use a graphing calculator.
• x 2y z 14
• -3x 3y 5z -22
• 11x 4y 7z 35

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• Solve the matrix equation.
• 6)

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• 4.6 Assignment
• Page 224 (13-25) odd, 33, 34, 35, 36, 37, 38, 39,
  40

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Unit 4 ReviewUsing Matrices
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• Unit 4 Test is worth 100 points
• Covers sections 4.1A, 4.1, 4.2, 4.3, 4.4, 4.5,
  4.6
• Study notes and hw
• Unit 4 Test Review
• Page 245 (1, 3, 4, 5, 7, 8, 9, 10), (11-47) odd,
• For 29, 31, 33 use expansion by minors and
  diagonals if possible
• For 47 use calculator to solve.
• Page 191 (25) previous hw problem
• Page 203 (24) previous hw problem
• Page 209 (25) previous hw problem

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• Items on the Test
• Matrix
• Element
• Dimensions
• Transformations
• Dilation
• Translation
• Rotation
• Determinant
• Expansion by Minors
• Diagonals
• Identity Matrix
• Inverse Matrix
• Matrix Equations