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Algebra 2: Lesson 5 Using Matrices to Organize Data and Solve Problems

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Warm-up p. 29 #1-5 1. The Additive _______ Property states that a + (-a) = 0 2. Add 16.5 – (-24.8) 3. Solve: 4 – 3y = 16 4. True or False: By the Commutative Property: j – k = k – j 5. Simplify: -4(x + 1)+ 3(2x – 7)

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Warm-up p. 29 #1-5 1. The Additive Inverse Property states that a + (- a) = 0 2. Add 16.5 – (-24.8) 41.3 3. Solve: 4 – 3y = 16 4 – 16 = 3y; -12 = 3y; - 4=y 4. True or False: By the Commutative Property: j – k = k – j 5. Simplify: -4(x + 1)+ 3(2x – 7) -4x – 4 + 6x – 21 = 2x - 25

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New Concept: Matrix A matrix is a rectangular array of numbers. The number of rows and columns in a matrix gives the dimensions of the matrix. A matrix with “r” rows and “c” columns is a matrix of dimension “r × c”. B = -3 -1 -2 2 -5 -4 Row #1 Row #2 Column #1 Column #3 Column #2

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Give the dimensions of each matrix.

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3 × 2 4 × 1 2× 3

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Elements of matrices Each member of the matrix is called an element and has a unique address. For example, in matrix A, a 43 is 5. What element is located at a 23 ?

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Matrix Addition To add two matrices of the same dimension, add each element in the first matrix to the element that is in the same location in the second matrix.

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Zero Matrix A zero matrix is formed when a matrix is added with its additive inverse matrix. matrix additive inverse matrix zero matrix

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Matrix Subtraction To subtract two matrices of the same dimensions, A – B, take the opposite, or additive inverse, of B and add it to A.

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Matrix Subtraction To subtract two matrices of the same dimensions, A – B, take the opposite, or additive inverse, of B and add it to A.

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Example 2 Find the additive inverse matrix of A. Add: -A + B Subtract: A – B. A = -1 2 -5 0 -4 3 B = -3 -1 -2 2 -5 -4

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Example 2 A = -1 2 -5 0 -4 3 B = -3 -1 -2 2 -5 -4 -A = 1 -2 5 0 4 -3 -A + B= -2 -3 3 2 -1 -7 A – B= 2 3 -3 -2 1 7

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Ex. 3: Solving a Matrix Equation Rewrite the equation as a subtraction equation. Subtract the matrices. -5 2 -4 3 + X = -1 -2 -5 -4 -5 2 -4 3 = X -1 -2 -5 -4 – 4 -4 -1 -7 X =

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Ex 4: Solving for Variables in Matrices Equal matrices have equal elements in matching locations. Write equations to make matching locations equal. a+12 = 18; a = 6 2b = -14; b = -7 23 = a + c; 23 = 6 + c; 23 - 6 = c; c = 17 d = 3b; d = 3(-7); d = -21 a + 12 2b 23 d = 18 -14 a + c 3b

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Scalar Multiplication A scalar is a constant by which a matrix is multiplied. Scalar Multiplication is analogous to repeated Matrix Addition. To multiply matrix A by scalar “n”, multiply every element of A by n.

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Ex. 4: Scalar Multiplication -5 2 -4 3 Evaluate : -2 M M =

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Ex. 4: Scalar Multiplication -5 2 -4 3 -2 -10 -4 -8 -6 = -5 2 -4 3 Evaluate : -2 M M =

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Partner Practice page 32 Lesson Practice a - f Individual Practice page 33 #1-29 odd

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