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**Adding & Subtracting Matrices**

Brought to you by Tutorial Services – The Math Center

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**In this Workshop you will:**

Matrices In this Workshop you will: Learn the definition of a matrix. Identify elements of a matrix. Learn how to add matrices. Learn how to subtract matrices. Learn how to solve variable expressions using addition and subtraction of matrices.

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Definition of a Matrix A matrix is a rectangular or square array of elements arranged in rows and columns. Numbers in a matrix are called its entries or elements. NOTE: Entries may be numerical or variable expressions.

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**Elements of a Matrix amn= any element in row m and column n**

m= number of rows n= number of columns amn= any element in row m and column n m×n= dimension of a matrix

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Addition If two or more matrices have the same order (same number of rows and columns) matrices may be added to their corresponding entries.

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Example 1: Find A + B Solution:

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Subtraction Like in addition, matrices that have the same order may be subtracted from their corresponding entries.

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Example 2: Find A - B Solution:

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**Variables in Matrices Use A + B = C to solve for x, y, and z.**

Solution: Add elements in matrix A with elements in Matrix B Rewrite elements in matrix A+B as variable expressions

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**Each Element in Matrix A+B corresponds to an element in matrix C**

Each Element in Matrix A+B corresponds to an element in matrix C. Therefore, the solutions can be found by treating each element as a linear equation and solving for the indicated variable. NOTE: Once x and y are found, there is no need to use A21 +B21 = C21 to solve. A11+ B11 = C11 A12+ B12 = C12 A22+ B22 = C22

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**Matrices Links Adding and Subtracting Matrices Handout**

Matrices Quiz Multiplying and Dividing Matrices Workshop Multiplying Matrices Handout Gauss-Jordan Workshop Gauss-Jordan Method Handout Inverse Matrix Handout

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