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Adding & Subtracting Matrices

Adding & Subtracting Matrices. Brought to you by Tutorial Services – The Math Center. 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.

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Adding & Subtracting Matrices

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  1. Adding & Subtracting Matrices Brought to you by Tutorial Services – The Math Center

  2. 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.

  3. 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.

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

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

  6. Example 1: Find A + B Solution:

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

  8. Example 2: Find A - B Solution:

  9. Variables in Matrices • Use A + B = C to solvefor x, y, and z. • Solution: • Add elements in matrix A with elements in Matrix B • Rewrite elements in matrix A+B as variable expressions

  10. 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

  11. Matrices Links • Adding and Subtracting Matrices Handout • 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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