1. Let A € Mmxp and B € Mpxn. Recall that the definition of matrix multiplication gives that the (i, j)-entry of the product AB is P [AB]ij = Σ Aik Bkj. k=1 Use the definition of matrix multiplication to show that (AB)¹ = BT AT.
1. Let A € Mmxp and B € Mpxn. Recall that the definition of matrix multiplication gives that the (i, j)-entry of the product AB is P [AB]ij = Σ Aik Bkj. k=1 Use the definition of matrix multiplication to show that (AB)¹ = BT AT.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section: Chapter Questions
Problem 17RQ
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![1. Let A € Mmxp and B € Mpxn. Recall that the definition of matrix multiplication gives that
the (i, j)-entry of the product AB is
P
[AB]ij = Σ AikBkj.
k=1
Use the definition of matrix multiplication to show that (AB)T = BT AT.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb04829d0-4645-426e-bf1a-7ada40b0786f%2F14e0011a-c1df-461c-bd2a-c2c5d4ef5b3c%2F3ch1tyi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Let A € Mmxp and B € Mpxn. Recall that the definition of matrix multiplication gives that
the (i, j)-entry of the product AB is
P
[AB]ij = Σ AikBkj.
k=1
Use the definition of matrix multiplication to show that (AB)T = BT AT.
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