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Let A = [a] and B = [bij] be two diagonal nx n matrices. Then the ijth entry of the product AB is Cij = 0 k = 1 If the ith row of A has all zero entries, evaluate the entries aik for all k = 1, 2, ..., n. aik = Evaluate the entries cj for all j = 1, 2,..., n. Cij = Thus, if the ith row of A has all zero entries, then the ith row of AB has all zero entries. Give an example using 2 x 2 matrices to show that the converse is not true. 0 0 18 10 B = 3 B = T

Let A = [a] and B = [bij] be two diagonal nx n matrices. Then the ijth entry of the product AB is Cij = 0 k = 1 If the ith row of A has all zero entries, evaluate the entries aik for all k = 1, 2, ..., n. aik = Evaluate the entries cj for all j = 1, 2,..., n. Cij = Thus, if the ith row of A has all zero entries, then the ith row of AB has all zero entries. Give an example using 2 x 2 matrices to show that the converse is not true. 0 0 18 10 B = 3 B = T

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let A and B be nxn matrices. Show that if the ith row of A has all zero entries, then the ith row of AB will have all zero entries. Let A = [a] and B = [bj] be two diagonal n x n matrices. Then the ijth entry of the product AB is Cij = 0 If the ith row of A has all zero entries, evaluate the entries aik for all k = 1, 2, ..., n. aik = k = 1 Evaluate the entries cj for all j = 1, 2,..., n. Cij Thus, if the ith row of A has all zero entries, then the ith row of AB has all zero entries. Give an example using 2 x 2 matrices to show that the converse is not true. 1 2 0 0 34 18 10 B = B = ↓ 1
Transcribed Image Text:Let A and B be nxn matrices. Show that if the ith row of A has all zero entries, then the ith row of AB will have all zero entries. Let A = [a] and B = [bj] be two diagonal n x n matrices. Then the ijth entry of the product AB is Cij = 0 If the ith row of A has all zero entries, evaluate the entries aik for all k = 1, 2, ..., n. aik = k = 1 Evaluate the entries cj for all j = 1, 2,..., n. Cij Thus, if the ith row of A has all zero entries, then the ith row of AB has all zero entries. Give an example using 2 x 2 matrices to show that the converse is not true. 1 2 0 0 34 18 10 B = B = ↓ 1
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