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7.3

7.3. Matrices. Matrix. A matrix is a rectangular array of elements. An array is a systematic arrangement of numbers or symbols in rows and columns. Matrices (the plural of matrix) may be used to display information and to solve systems of linear equations.

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7.3

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  1. 7.3 Matrices

  2. Matrix • A matrix is a rectangular array of elements. • An array is a systematic arrangement of numbers or symbols in rows and columns. • Matrices (the plural of matrix) may be used to display information and to solve systems of linear equations. • The numbers in the rows and columns of a matrix are called the elements of the matrix.

  3. Dimensions of a Matrix • The dimensions of a matrix may be indicated with the notation r s, where r is the number of rows and s is the number of columns of a matrix. • A matrix that contains the same number of rows and columns is called a square matrix. Example: 3  3 square matrices:

  4. Addition and Subtraction of Matrices • Two matrices can only be added or subtracted if they have the same dimensions. • The corresponding elements of the two matrices are either added or subtracted.

  5. Example: Adding Matrices Example: Find A + B. Solution: A + B

  6. Practice Problem: Determine A - B

  7. Scalar Multiplication • A matrix may be multiplied by a real number, a scalar, by multiplying each entry in the matrix by the real number. Determine 3A

  8. Multiplication of Matrices • Multiplication of matrices is possible only when the number of columns in the first matrix is the same as the number of rows of the second matrix. • In general,

  9. Example: Multiplying Matrices Solution:

  10. Practice: Determine A X B

  11. Example: Identity Matrix in Multiplication Use the multiplicative identity matrix for a 2  2 matrix and matrix A to show that Solution:The identity matrix is

  12. Example: Identity Matrix in Multiplication continued

  13. Multiplicative Identity Matrix • Square matrices have a multiplicative identity matrix. • The following are the multiplicative identity for a 2 by 2 and a 3 by 3 matrix. For any square matrix A, A I = I  A = A.

  14. Homework P. 411 # 12 – 54 (x3)

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