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14111cn2.12-13 - c Kendra Kilmer Section 2.5 Multiplication...

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c Kendra Kilmer August 18, 2011 Section 2.5 - Multiplication of Matrices How to Multiply Matrices ( C = AB ): (a) Check to see if the number of columns of matrix A is equal to the number of rows in matrix B . If this condition is satisfied, the multiplication is a valid operation. The resulting matrix C will have the same number of rows as A and the same number of columns as B . (b) Compute each entry in the resulting matrix C . The entry c i j is found by using the i th row of matrix A and the j th column of matrix B as shown in the next example. Example 1: Let A = 1 2 3 4 B = 4 2 1 3 Find C where C = AB . Note: In general, AB 6 = BA Example 2: Given the following matrices with given dimensions, determine whether each of the following is a valid matrix operation. A 2 × 3 B 3 × 5 C 5 × 2 D 2 × 3 a) AB - C b) 3 AC - D c) CD - 5 B T d) DA - 3 C e) D - BC 12
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c Kendra Kilmer August 18, 2011 Definition: The identity matrix of size n has n rows and n columns. It has 1’s along the main diagonal and 0’s everywhere else.
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