2¹j and bij 2-ij for (a) Let the entries of A and B be given by aij = 1≤i, j≤ 20. Let C = AB. Compute c11,11. (b) For A, B, C as in part (a), compute c9,6- (c) Let the entries of A and B be given by aij = 2¹ and bij = 2-¹ for 1≤i, j≤ N. Let C = AB. Give a general formula for cij that is valid for any (i, j) with 1 ≤ i, j ≤ N. (d) Let the entries of A and B be given by aj = wi and bij w-ij for 1 ≤i, j≤N, where w is a fixed complex number. Let C = AB Give a general formula for cij that is valid for any (i, j) with 1 ≤ i, j ≤ N. =
2¹j and bij 2-ij for (a) Let the entries of A and B be given by aij = 1≤i, j≤ 20. Let C = AB. Compute c11,11. (b) For A, B, C as in part (a), compute c9,6- (c) Let the entries of A and B be given by aij = 2¹ and bij = 2-¹ for 1≤i, j≤ N. Let C = AB. Give a general formula for cij that is valid for any (i, j) with 1 ≤ i, j ≤ N. (d) Let the entries of A and B be given by aj = wi and bij w-ij for 1 ≤i, j≤N, where w is a fixed complex number. Let C = AB Give a general formula for cij that is valid for any (i, j) with 1 ≤ i, j ≤ N. =
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,C,D 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 11.2.4.
2ij and bij
(a) Let the entries of A and B be given by ai.j =
1 ≤i, j≤ 20. Let C = AB. Compute c11,11.
(b) For A, B, C as in part (a), compute c9,6.
2-ij for
=
(c) Let the entries of A and B be given by aij = 2¹ and bij
1 ≤i, j≤ N. Let C = AB. Give a general formula for cij that is valid
for any (i, j) with 1 ≤ i, j < N.
2-ij for
=
w-ij for
=
(d) Let the entries of A and B be given by aj = wij and bij
1 ≤i, j≤ N, where w is a fixed complex number. Let C = AB Give a
general formula for cij that is valid for any (i, j) with 1 ≤i, j≤ N.
Expert Solution
Step 1 Part a
Let A and B are 20 x 20 matrices
A = [( ai,j )] and B = [(bi,j )]
ai,j = 2ij
bi,j = 2-ij
C = AB is the product of matrices A and B
C is a 20 x 20 matrix
The ( i , j) th entry of C is ci,j
c11,11 is determined by taking the sum of products of each element in the 11 th row of A and the corresponding elements of 11 th column of B.
c11,11 = a11,1 b1,11 + a11,2 b2,11 +........+ a11,20 b 20,11
Step by step
Solved in 3 steps
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