Let's show how this formula works in a specific case. Suppose A is a 3 x 3 matrix and B is a 3 x 2 matrix as in our previous example, then the result of the product AB is a 3 x 2 matrix that we can call C. Now suppose we want to find the entry on the third row in the second column of C, then we would compute: 3 C3,2=a3,kbk,2 k=1 =a3,1b1,2 + a3,2b2,2 + a3,303,2. Sure enough, when we look at the long version we wrote earlier for the product AB our result matches the entry on the second row, third column. The above formula makes it possible to calculate individual matrix ele- ments, without having to compute the entire matrix.
Let's show how this formula works in a specific case. Suppose A is a 3 x 3 matrix and B is a 3 x 2 matrix as in our previous example, then the result of the product AB is a 3 x 2 matrix that we can call C. Now suppose we want to find the entry on the third row in the second column of C, then we would compute: 3 C3,2=a3,kbk,2 k=1 =a3,1b1,2 + a3,2b2,2 + a3,303,2. Sure enough, when we look at the long version we wrote earlier for the product AB our result matches the entry on the second row, third column. The above formula makes it possible to calculate individual matrix ele- ments, without having to compute the entire matrix.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.3: Matrix Algebra
Problem 85E: Determine if the statement is true or false. If the statement is false, then correct it and make it...
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