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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.

- 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

- Naming the dimensions of the matrix

- Scalar Multiplication of a Matrix
- 1) 2)

- Solve for the variables
- 3) 4)

- 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.

- 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.

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

4.1A MatricesGraphing Technology

- Enter matrix A in a graphing calculator.
- 1)

- Enter matrix B in a graphing calculator. Then

find 2A, AB, B AB, the determinant of A and the

inverse of A. - 2)

- 4.1A Assignment
- Page 185 (1-18)

4.2 Adding and Subtracting MatricesNeed Graph

Paper!

- Objective
- To add and subtract matrices

- Vocabulary
- Translation- a figure is moved from one location

to another without changing size, shape, or

orientation.

- Determine if you can add or subtract matrices

and evaluate if possible. - 1.) 2.)

- Determine if you can add or subtract matrices

and evaluate if possible. - 3.) 4.)

- 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.

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

4.3 Multiplying MatricesNeed Graph Paper!

- Objective
- To multiply matrices

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

- When can you add or subtract matrices?

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

- Multiply matrices if possible.
- 1) 2)

- 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.

- 4.3 Assignment
- Page 202 (18-24), (26-27), 35, 36, 40, 41, 42,

43, 44, 45, 46

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.

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

- Evaluate by using diagonals.
- 3) 4)

- 5) Find the area of the triangle whose vertices

are located at (3, -4), (5, 4), and (-3, 2) by

using matrices.

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

41, 42

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

- Vocabulary
- Identity Matrix- the matrix that has a value of

one when you find the determinant of it.

- Find I so N(I) N.
- 1) 2)

- 3) 4)

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

38, 39

4.6 Using Matrices to Solve Systems of Equations

- Objective
- To solve systems of linear equations by using

inverse matrices.

- 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

- Use a matrix equation to solve the system of

equations. - 7x 5y 3
- 3x 2y 22

- Use a matrix equation to solve the system of

equations. - 4) 4x 12y 7
- x 6y 9

- 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

- Solve the matrix equation.
- 6)

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

40

Unit 4 ReviewUsing Matrices

- 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

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

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