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
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F08e5da1f-7ff5-4a3a-ae83-22ae4b63090a%2Fc0c2c3ae-e65f-46ee-bcdd-406d346376a3%2Fmrdcxo8_processed.png&w=3840&q=75)
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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