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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please do part A,B,C and please show step by step and explain
Transcribed Image Text: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
€3,2 = 93,kbk,2
k=1
=a3,101,2 +03,2b2,2 + a3,3b3,2-
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.
Transcribed Image Text:Exercise 11.2.5.
= zij
(a) Let z = cis(π/4), and let the entries of A and B be given by aij =
and bijz-¹ for 1 ≤i, j ≤ 8. Let C = AB Compute C4,4 and c3,5.
=
(b) Let z = cis(27/N), and let the entries of A and B be given by aj = zij
z¯¹ for 1 ≤ i, j≤ N. Let C = AB Give a general formula
which is valid for all k with 1 ≤ k ≤ N.
=
and bij
for Ck,k
(c) Let z = cis(27/N), and let the entries of A and B be given by aj = z²j
and bij = z-¹ for 1 ≤i, j≤ N. Let C = AB Give a general formula
for Ck+1,k which is valid for all k with 1 ≤ k ≤ N-1.
Expert Solution
Step 1
(a) , let the entries of A and B be defined as for .
To Find: .
(b) let and the entries of A and B be defined as for .
To Find: A general rule for .
(c) let and the entries of A and B be defined as for .
To Find: A general rule for .
Step by step
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