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Published byNigel Tyler Modified over 6 years ago

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**4.2 Adding and Subtracting Matrices 4.3 Matrix Multiplication**

Date: _____________

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**Adding and Subtracting Matrices**

Must be the same dimensions Add or Subtract corresponding elements

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Adding Matrices To add matrices, add all the corresponding elements. 4 -2 7 3 2 5 -3 7 + = 12 -3

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**− = 4 -2 7 3 2 5 -3 1 -4 2 3 Subtracting Matrices**

To subtract matrices, subtract all the corresponding elements. 4 -2 7 3 2 5 -3 1 -4 − = 2 3

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12 -4 13 -7 -8 19 23 14 20 -23 − = -10 -21

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**Dimensions are not the same.**

12 -2 4 7 − = 9 -3 Not Possible! Dimensions are not the same.

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**Solving a Matrix Equation**

Get the variable by itself The variable is representing a matrix Subtracting matrices

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**Solving a Matrix Equation**

Subtracting matrices 4 -8 -1 -1 11 1

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**Solving Equation Matrices**

Each corresponding element is equal

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**Muliplying Matrices Same concept as the Distributive Property**

Scalar Multiplication – multiply a matrix by a factor. 45 -36 30 60 -30 21 Same concept as the Distributive Property

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**Matrix Multiplication**

Suppose that you want to multiply matrices A and B. A has dimensions m x n and B has dimensions p x q. If multiplication is possible, the answer will have dimensions m x q. m x n p x q If n = p, multiplication is possible.

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**multiplication is possible.**

2 9 5 8 7 8 2 3 answer will be 2 x 2 2 x 2 2 x 2 multiplication is possible. 28 43 (2)(8) + (9)(3) (2)(5) + (9)(2) = 51 80 (7)(5) + (8)(2) (7)(8) + (8)(3)

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**DON’T FORGET YOUR CALCULATOR!!!**

FUN? DON’T FORGET YOUR CALCULATOR!!!

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