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 = Σa3.bk,2 k=1 =a3,101,2 + a3,2b2,2 +03,303,2- 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. Exercise 11.2.2. (a) Let the entries of A be given by ai.j = Vi+j for 1 ≤ i, j ≤ 100. Let C = A.A (we can also write C = A²). Compute €10,10- = (b) Let the entries of A and B be given by aij = (i+j)² and bij 1≤i, j≤ 27. Let C = A B Compute €8,8. for (c) For the matrices A and B in part (b), give a general formula for Ck,k, 1 ≤ < 27 wh
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 = Σa3.bk,2 k=1 =a3,101,2 + a3,2b2,2 +03,303,2- 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. Exercise 11.2.2. (a) Let the entries of A be given by ai.j = Vi+j for 1 ≤ i, j ≤ 100. Let C = A.A (we can also write C = A²). Compute €10,10- = (b) Let the entries of A and B be given by aij = (i+j)² and bij 1≤i, j≤ 27. Let C = A B Compute €8,8. for (c) For the matrices A and B in part (b), give a general formula for Ck,k, 1 ≤ < 27 wh
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 B and 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.
Exercise 11.2.2.
(a) Let the entries of A be given by aj = Vi+j for 1 ≤i, j≤ 100. Let
C = A.A (we can also write C = A²). Compute €10,10-
(b) Let the entries of A and B be given by ai.j = (i+j)² and bij = for
1 ≤i, j≤ 27. Let C = A - B Compute €8,8.
(c) For the matrices A and B in part (b), give a general formula for ck,k,1 <
k≤ 27 where C= AB.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
