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Lesson 11-1 Matrix Basics and Augmented Matrices

Lesson 11-1 Matrix Basics and Augmented Matrices. Objective: To learn to solve systems of linear equation using matrices. Matrices. A rectangular array of numbers is called a matrix (plural is matrices) It is defined by the number of rows (m) and the number of columns (n) “m by n matrix”

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Lesson 11-1 Matrix Basics and Augmented Matrices

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  1. Lesson 11-1 Matrix Basics and Augmented Matrices Objective: To learn to solve systems of linear equation using matrices.

  2. Matrices • A rectangular array of numbers is called a matrix (plural is matrices) • It is defined by the number of rows (m) and the number of columns(n) “m by n matrix” • Example: is a 2 x 3 matrix 1 0 5 2 3 4

  3. Matrices • Each number in the matrix has a position A = • Each item in the matrix is called an element a 11 a 12 a 13 a 21 a 22 a 23

  4. What is the dimension of each matrix? (or square matrix) 3 x 3 (Also called a column matrix) 1 x 4 3 x 5 2 x 2 (or square matrix) 4 x 1 (Also called a row matrix)

  5. Warm-Up Give the dimensions of each matrix. 2) 1) Identify the entry at each location of the matrix below. 3) b12 4) b21 5) b32

  6. Warm up • Find the dimensions of the following matrices: • 1. 2. • 3. For the first matrix find a21

  7. Augmented Matrices Augmented matrix has the coefficients of all the variables (in order) along with the answers in the last column. • System of Linear Equation • x -2y + 2z = -4 • x + y – 7z = 8 • -x -4y + 16z = -20 • expressed in a matrix: -2 2 • 1 -7 • -4 16

  8. Using the Calculator to Solve • [2nd] [matrix] EDIT[ENTER] • MATRIX [A] IS A 3 x 4 matrix (3 rows x 4 columns) • then enter all the data into the matrix • Once data is entered, quit then • [2nd] [matrix] MATH • scroll down to B: rref [ENTER] [2ND] [MATRIX] [A] [ENTER] • You will get a new matrix - the last column is your answer for x, y and z.

  9. Practice: • 1. 4x + 6y = 0 2. 6x - 4y + 2z = -4 3. 5x - 5y + 5z = 10 • 8x - 2y = 7 2x - 2y + 6z = 10 5x - 5z = 5 • 2x + 2y + 2z = -2 5y + 10z = 0

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