Definition 1 Multiplying Two Matrices For A Roxn And E R We Have Defined Matrix Vector Multiplication Now Consi 1 (66.63 KiB) Viewed 225 times
Definition 1. Multiplying two matrices. For A € Rºxn and ✓ E R", we have defined matrix vector multiplication. Now consider another matrix BE RnXP which has p columns, denoted as 61, 62, ..., bp. Then we can multiply A to each column of B because the sizes match: we get another
p column vectors of size m as A71, A72, ... AÕ1, AÕ2, . , Aõp. If we put together these vectors AĞI, AZ2, ... , Aõp, we get another matrix of size m xp and define this new matrix as A multiplied to B (or product of A and B), denoted as AB. For example, A= =(-12) ),B= ( 0 1 1 3 → AB 27 0 -1 Now compute AB for the following matrices: (a) 1 2 3 A= -1 10 0 B= 0 1 -5 1 0 -1 1 0 1 1 0 -1 (b) 1 2 3 4 -1 1 0 2 B = 1 0 1 -1 1 0 0 1 - 1 2 0 1 2
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