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.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.3: Matrix Algebra
Problem 85E: Determine if the statement is true or false. If the statement is false, then correct it and make it...
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
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
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning