Matrix multiplication is only defined when the number of columns of the first matrix equals the number of rows of the second matrix. The document provides examples of determining if matrix products are defined based on their dimensions and calculating the dimensions of the products. If the product is defined, the dimensions are stated as the number of rows of the first matrix and columns of the second.

1. Pg 168 Matrix multiplication is defined only if the number of columns of the first matrix is equal to the number of rows of the second matrix.

2. Determine whether the product of is defined. If so, state the dimensions of the product. A • B = AB 3  4 4  2 3  2 The inner dimensions are equal so the matrix product is defined. The dimensions of the product are 3  2. Example 3-1a

3. Determine whether the product of is defined. If so, state the dimensions of the product. A • B 3  2 4  3 The inner dimensions are not equal, so the matrix product is not defined. Example 3-1b

4. Determine whether each matrix product is defined. If so, state the dimensions of the product. a. b. Answer: The matrix product is defined. The dimensions are 3  3. Answer: The matrix product is not defined. Example 3-1c

5. Find RS if Example 3-2d

6. Example 3-4c

7. Find A(B + C) if Substitution Add corresponding elements. Example 3-5f