Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN: 9780133594140
Author: James Kurose, Keith Ross
Publisher: PEARSON
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Transcribed Image Text:Perform the following Matrix Operations for the predefined matrices.
Given the System of equations:
2х + 4у —52 + Зw %3D— 33
Зх + 5у—2г + бw %3D — 37
x- 2y + 4z – 2w = 25
Зх + 5у-3г + Зw %3D - 28
Write the systems as Ax = b, where A is the coefficient matrix and b is the vector for the constants.
1. Encode the Matrix A and the column vector b.
2. Solve for Determinant of A.
3. Find the Inverse of A.
4. Form the Reduced Row Echelon of A.
5. Find the number of rows and number of columns of Ab.
6. Find the sum of the columns of A.
7. In each of the columns of A, find the highest values and its indices.
8. Augment A with b;
9. Find bVA
10. Form the Reduced Row Echelon of Ab.
11. Extract the Last Column of the Reduced Row Echelon Form of Ab.
12. Create a matrix A whose elements are the same as matrix A, but the first column is the column vector b.
13. Create a matrix A whose elements are the same as matrix A, but the second column is the column vector b.
14. Create a matrix A whose elements are the same as matrix A, but the third column is the column vector
![1 X Encode the Matrix A and the column vector b.
2 A= [2 4 -5 3;
35 -2 6;
1 -2 4 -2;
35 -3 3]
4
6b = [-33;-37; 25;-28]
7 % Solve for Deterninant of A. Set as dA.
8 dA = det (A)
9 X Find the Inverse of A. set as iA.
10 1A- inv(A)
11 X Form the Reduced Row Echelon of A. Set as rA.
12 rA = rref(A)
13 XFind the number of rows and nunber of columns of Ab. set as rowA and colA.
14 [rowA colA] = size([A b])
15 % Find the sum of the colunns of A. Set as SumA.
16 suna = sum(A, 1)
17 XIn each of the columns of A, find the highest values and its indices.Set as higha and locA.
18 [highA, locA] = nax(A)
19 XAugnent A with b; Set as Ab.
20 Ab = [A,b]
21 % Find b\A. Set as Rooti1.
22 Root1 = b\A
23 XForm the Reduced Row Echelon Form of Ab. Set as refAb.
24 refAb = rref(Ab)
25 XExtract the last colunn of refAb.Set as Root2.
25 Root2 = refAb(:,end)
27 XCreate a natrix A whose elements are the same as matrix A, but the first column is the column vector b. Set as Ax.
28 A1-A;
29 A2-A;
30 A3=A;
31 A4-A;
32 A1(:,1) = b;
33 Ax = A1
34 XCreate a matrix A whose elements are the same as matrix A, but the second column is the column vector b. Set as Ay.
35 A2(:,2) = b;
36 Ay = A2
37 XCreate a natrix A whose elements are the same as matrix A, but the third column is the column vector b. Set as Az.
38 A3(:,3) = b;
39 Az = A3
4e XCreate a natrix A whose elements are the same as matrix A, but the fourth colunn is the column vector b. Set as Aw.
41 A4(:,3) = b;
42 Aw A4
43 XFind x using Craner's Rule.
44 x = det(Ax)/det (A);
45 XFind y using Craner's Rule.
46 y = det(Ay)/det (A);
47 XFind z using Craner's Rule.
48 z = det(Az)/det (A);
49 XFind w using Craner's Rule.
se w= det (Aw)/det (A);
51 XCombine x,y,z and w as column vector Root3.
52 disp("x= 1")
53 disp(x)
54 disp("y = -2")
55 disp(y)
56 disp("2 = 3")
57 disp(2)
58 disp("w 4")
59 disp(w)](https://content.bartleby.com/qna-images/question/db5ef6b4-a1ff-42dd-8003-47471ac11388/8fc79cf8-1af2-4637-b600-5c94732af3a8/a102cki_processed.png)
Transcribed Image Text:1 X Encode the Matrix A and the column vector b.
2 A= [2 4 -5 3;
35 -2 6;
1 -2 4 -2;
35 -3 3]
4
6b = [-33;-37; 25;-28]
7 % Solve for Deterninant of A. Set as dA.
8 dA = det (A)
9 X Find the Inverse of A. set as iA.
10 1A- inv(A)
11 X Form the Reduced Row Echelon of A. Set as rA.
12 rA = rref(A)
13 XFind the number of rows and nunber of columns of Ab. set as rowA and colA.
14 [rowA colA] = size([A b])
15 % Find the sum of the colunns of A. Set as SumA.
16 suna = sum(A, 1)
17 XIn each of the columns of A, find the highest values and its indices.Set as higha and locA.
18 [highA, locA] = nax(A)
19 XAugnent A with b; Set as Ab.
20 Ab = [A,b]
21 % Find b\A. Set as Rooti1.
22 Root1 = b\A
23 XForm the Reduced Row Echelon Form of Ab. Set as refAb.
24 refAb = rref(Ab)
25 XExtract the last colunn of refAb.Set as Root2.
25 Root2 = refAb(:,end)
27 XCreate a natrix A whose elements are the same as matrix A, but the first column is the column vector b. Set as Ax.
28 A1-A;
29 A2-A;
30 A3=A;
31 A4-A;
32 A1(:,1) = b;
33 Ax = A1
34 XCreate a matrix A whose elements are the same as matrix A, but the second column is the column vector b. Set as Ay.
35 A2(:,2) = b;
36 Ay = A2
37 XCreate a natrix A whose elements are the same as matrix A, but the third column is the column vector b. Set as Az.
38 A3(:,3) = b;
39 Az = A3
4e XCreate a natrix A whose elements are the same as matrix A, but the fourth colunn is the column vector b. Set as Aw.
41 A4(:,3) = b;
42 Aw A4
43 XFind x using Craner's Rule.
44 x = det(Ax)/det (A);
45 XFind y using Craner's Rule.
46 y = det(Ay)/det (A);
47 XFind z using Craner's Rule.
48 z = det(Az)/det (A);
49 XFind w using Craner's Rule.
se w= det (Aw)/det (A);
51 XCombine x,y,z and w as column vector Root3.
52 disp("x= 1")
53 disp(x)
54 disp("y = -2")
55 disp(y)
56 disp("2 = 3")
57 disp(2)
58 disp("w 4")
59 disp(w)
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