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Matrix Multiplication Explained | Example Problems & Solutions

Learn how to multiply matrices step by step with detailed examples. Understand the rules for matrix multiplication and practice solving problems for better clarity. Explore the order of matrices and the process of multiplying them effectively.

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Matrix Multiplication Explained | Example Problems & Solutions

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  1. Matrices - Multiplication • Assume that matrix A is of order m  n and matrix B is of order p  q. To determine whether or not A can be multiplied times B, write the matrices with their orders ... A B m  n p  q. • If the two inside numbers are the same, then matrix multiplication is possible. • When multiplication is possible, the resulting matrix will have an order determined by the outside numbers.

  2. Matrices - Multiplication • Example 1: • Find AB where A and B are given by ... 2  3 3  4 • Since the inside numbers are the same, the multiplication • is possible. • The resulting matrix will be 2  4. Slide 2

  3. 2  4 Matrices - Multiplication • The process of multiplying is as follows: • To get the first entry of the product matrix, note that it is the row 1 column 1 entry.  • Multiply row 1 of matrix A times column 1 of matrix B. Slide 3

  4. Matrices - Multiplication • Multiply pairs of numbers by moving across the row and down the column, and add the products. (1)(1) + (-2)(3) + (3)(-2) = 1 - 6 - 6 = -11 Slide 4

  5. Matrices - Multiplication  • The next entry of the product matrix is in row 1 and column 2. • Multiplying as before with row 1 of matrix A and column 2 of matrix B ... (1)(0) + (-2)(-2) + (3)(-1) = 1 Slide 5

  6. Matrices - Multiplication The row 1 column 3 entry is ... The row 1 column 4 entry is ... The row 2 column 1 entry is ... The row 2 column 2 entry is ... The row 2 column 3 entry is ... The row 2 column 4 entry is ... Slide 6

  7. Matrices - Multiplication • Thus, the product of the matrices is ... Slide 7

  8. Matrices - Multiplication • Example 2: • Find CD where C and D are given by ... • The answer is ... Slide 8

  9. Matrices - Multiplication END OF PRESENTATION Click to rerun the slideshow.

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